// The Memory Curse in LLM Agents // (bookmark it) Long histories apparently degrades agents as they become increasingly history-following and risk-minimizing. Across 7 LLMs and 4 social dilemma games over 500 rounds, expanding accessible history degraded cooperation in 18 of 28 model–game combinations. They call it the memory curse. Lexical analysis of 378,000 reasoning traces shows the mechanism: it’s not that agents become paranoid, it’s that forward-looking intent erodes. Long histories pull the model into reasoning about past slights instead of future payoffs. A LoRA adapter trained only on forward-looking traces mitigates the decay and transfers zero-shot to new games. Memory sanitization, keeping prompt length fixed but swapping in synthetic cooperative records, restores cooperation, proving the trigger is content, not length. And ablating explicit Chain-of-Thought often reduces the collapse, meaning deliberation actively amplifies the curse. Paper: https://arxiv.org/abs/2605.08060 Learn to build effective AI agents in our academy: https://academy.dair.ai

The Memory Curse: How Expanded Recall Erodes Cooperative Intent in LLM Agents

Source: https://arxiv.org/html/2605.08060 Jiayuan Liu1,2,Tianqin Li∗1,Shiyi Du∗1,Xin Luo∗3,Haoxuan Zeng3,Emanuel Tewolde1,2,Tai Sing Lee1,Tonghan Wang4,Carl Kingsford1,Vincent Conitzer1,2 1Carnegie Mellon University2Foundations of Cooperative AI Lab (FOCAL)3University of Michigan4Harvard University

{jiayuan4, tianqinl, shiyid}@cs.cmu.edu,{luosanj, zchx}@umich.edu,[email protected],[email protected],[email protected],[email protected],[email protected]

Abstract

Context window expansion is often treated as a straightforward capability upgrade for LLMs, but we find it systematically fails in multi-agent social dilemmas. Across 7 LLMs and 4 games over 500 rounds, expanding accessible history degrades cooperation in 18 of 28 model–game settings, a pattern we term thememory curse. We isolate the underlying mechanism through three analyses. First, lexical analysis of 378,000 reasoning traces associates this breakdown with eroding forward-looking intent rather than rising paranoia. We validate this using targeted fine-tuning as a cognitive probe: a LoRA adapter trained exclusively on forward-looking traces mitigates the decay and transfers zero-shot to distinct games. Second, memory sanitization holds prompt length fixed while replacing visible history with synthetic cooperative records, which restores cooperation substantially, proving the trigger is memory content, not length alone. Finally, ablating explicit Chain-of-Thought reasoning often reduces the collapse, showing that deliberation paradoxically amplifies the memory curse. Together, these results recast memory as an active determinant of multi-agent behavior: longer recall can either destabilize or support cooperation depending on the reasoning patterns it elicits.

1Introduction

The integration of large language models (LLMs) into multi-agent systems provides a powerful new substrate for simulating complex social, economic, and game-theoretic dynamics(Parket al.,2023; Xiet al.,2025). A central challenge within these multi-agent ecosystems is navigating social dilemmas (such as the Prisoner’s Dilemma or Trust Game) where individual short-term rationality conflicts with collective long-term welfare. Historically, classical game theory literature has relied on expansive interaction histories, coupled with an infinite horizon, to explain the mathematical feasibility of sustained cooperation (e.g., the Folk Theorem)(Fudenberg and Maskin,1986).

However, this classical assumption contradicts empirical realities in behavioral psychology. Rather than building trust,Maet al.(2021)demonstrated that an excessively long memory actually degrades cooperation, as human subjects become overwhelmed by historical noise and succumb to grudge-holding. Interestingly, human cognition naturally attempts to mitigate this vulnerability by relying on sparse, compressed representations of past events, essentially using “forgetting” as a mechanism to forgive and adapt. Artificial agents, by contrast, process dense, verbatim transcripts of history without any natural degradation. This structural difference in memory creates a profound question for the deployment of autonomous systems: does expanding an agent’s memory build necessary trust, or does a perfect historical ledger inevitably doom the system to unforgiving retaliation?

In this paper, we address this question by systematically studying how memory length affects cooperation in multi-agent LLM interactions. To evaluate this, we manipulate both the agents’ reasoning capabilities and their passive memory, adjusting the latter through varying history length (H​LHL) settings. (Figure1). While most prior work evaluates LLMs in repeated games over very short horizons, typically no more than 10 rounds(Akataet al.,2025; Brookins and DeBacker,2023; Li and Shirado,2025), such settings can obscure the effects of long interaction histories. We therefore scale the environments to 500-round repeated interactions.

Figure 1:Schematic of repeated social dilemma interactions between two LLM agents with shared memory.Our results reveal two distinct regimes. In some model–game combinations, sufficiently capable models sustain cooperation by correctly understanding the game structure and reasoning about the long-run consequences of reciprocity. Their behavior is forward-looking and aligns with the logic of the Folk Theorem(Fudenberg and Maskin,1986). In many other cases, however, increasing passive historical memory instead undermines long-term cooperation, producing a counterintuitive “memory curse”. In this regime, agents become increasingly history-following and risk-minimizing, which closely mirrors the human behavioral patterns reported byMaet al.(2021).

To summarize, our main contributions are as follows:

• •A large-scale empirical study of memory in long-horizon repeated social dilemmas with LLM agents.To our knowledge, this is the first systematic sweep of interaction memory length in repeated LLM social dilemmas at this scale. Our evaluation spans 7 different LLMs×\times4 repeated social dilemma games (involving 2 to 3 players)×\times9 history-length settings×\times3 seeds, where each interaction consists of 500 repeated rounds over an order of magnitude longer than prior evaluations(Akataet al.,2025; Brookins and DeBacker,2023; Li and Shirado,2025). Together with our asymmetric-length-memory, memory-sanitization, and forward-looking fine-tuning ablation experiments, the full study produces over 378,000 reasoning traces. We provide a sample of these traces in the Appendix and will release as a public resource for studying memory-cooperation dynamics in agent societies.
• •Answering whether more memory helps or hurts cooperation.We directly test the assumption that longer interaction history improves trust and coordination. Instead, we find that expanded memory often harms cooperation by making agents less forgiving and more defensive, while also identifying settings where longer memory still supports stable cooperation.
• •Revealing distinct behavioral regimes under memory expansion.We show that expanded memory induces qualitatively different cooperation regimes: some model–game settings remain highly cooperative, while others exhibit a “memory curse” in which longer recall promotes history-following, defensive reasoning, and cooperation collapse. This demonstrates that memory effects depend on model capability, game structure, and reasoning style, rather than context length alone.
• •Testing the forward-looking hypothesis through targeted fine-tuning.Using a LoRA intervention inspired byGandhiet al.(2025), we fine-tune a memory-cursed Mistral-7B model on forward-looking reasoning traces. This substantially mitigates cooperation decay at extended history lengths without compromising the general task ability (GSM8K, TriviaQA, HumanEval, and MBPP) and transfers zero-shot to untrained games, providing interventional evidence that forward-looking reasoning can reduce the memory curse.

2Related Work

LLMs in Social Dilemmas and Repeated Games.Prior work shows that LLM cooperation in repeated interaction is fragile and highly path-dependent.Akataet al.(2025)study finitely repeated2×22\times 2games and showed that LLMs can cooperate in self-interested settings such as the repeated Prisoner’s Dilemma, yet often become unforgiving after defection and struggle to keep adaptive cooperation. The success deteriorates further if the co-players across repetition rounds vary(Tewoldeet al.,2026). Furthermore,Piattiet al.(2024)showed that most LLM societies fail to maintain cooperation in social dilemma games. These studies suggest that LLM cooperation is often easier to maintain in the early stages than in later rounds.

Reasoning and Strategic Behavior of LLMs in Games.Duanet al.(2024)further showed in GTBench that strategic competence is uneven across game environments, and that explicit reasoning methods such as chain-of-thought (CoT)(Weiet al.,2022)or tree-of-thought(Yaoet al.,2023)do not reliably improve performance. More recently,Piedrahitaet al.(2025); Li and Shirado (2025)found that reasoning-oriented models can even cooperate less than non-reasoning models, tending toward individually rational but socially harmful behaviors and decisions. These findings suggest that reasoning is not uniformly beneficial for cooperation and will itself change the strategic style of LLM agents.

Memory Effects on Intelligence Systems.In parallel, memory has emerged as a powerful mechanism for enhancing the capabilities of AI systems. Prior to the LLM era, works such asWestonet al.(2014)andLiet al.(2022)explored explicit memory architectures to improve robustness and generalization, demonstrating that memory can serve as an orthogonal dimension for capability enhancement beyond parameter optimization. In the era of agentic AI, this line of research has expanded to include frameworks such as Retrieval-Augmented Generation (RAG;Lewiset al.(2020)), Memory-GPT(Packeret al.,2023), and a growing suite of evaluation benchmarks, including MemBench(Tanet al.,2025)and MemoryAgentBench(Huet al.,2025). Collectively, these works highlight the central role of memory in constructing more capable and adaptive intelligent systems. However, despite this progress, there remains a lack of large-scale, systematic studies evaluating the role of memory in multi-agent social dilemma settings, where multiple agents equipped with memory interact strategically over time.

Together, these studies show that cooperation in repeated interactions among LLM agents is difficult to maintain. However, it remains unknown how different bounded interaction-history lengths shape cooperative outcomes, including when longer history supports consistent cooperation and when it instead amplifies behavioral noise and drives cooperation collapse.

3Experiment Design and Settings

To empirically characterize cooperation regimes of LLM agents, we evaluated multiple LLMs across four classic social dilemma games. Specifically, we studied seven representative models: Gemma-3-12B, GPT-OSS-20B, GPT-OSS-120B, Llama-3.3-70B, Llama-4-Scout-17B, Mistral-7B, and Qwen2.5-Coder-32B, and four social dilemma environments: Prisoner’s Dilemma (PD), Traveler’s Dilemma (TD), Public Goods Game (PG), and Trust Game (TG). The full game definitions and the corresponding prompts are given in AppendixA.

In each experiment, two or three LLM agents instantiated from the same backbone model repeatedly play one of the four social dilemma games while sharing access to the history of all players’ past decisions. In this repeated game setting, the agents are very likely (e.g., 99%, agents know the probability) to play another round, and they will be playing with the same opponents. Specifically, we require the agents to aim for long-term cumulative rewards, to mitigate the tendency toward short-view defection. In addition, we instruct the models to reason in a chain-of-thought manner by (1) thinking through the game rule and history, (2) outputting their reasoning path, and (3) providing a final game decision. Across all games, the prompt explicitly tells agents that, after each round, the interaction will continue to the next round with a high preset probability (e.g., 99%). This creates a repeated-game setting in which agents believe they are very likely to play another round with the same opponent, thereby preserving incentives for reciprocity, retaliation, and trust repair. To study the effect of bounded memory, we vary the accessible interaction-history length (H​LHL), defined as the number of previous rounds whose decisions remain available to the agent. We then track both behavioral trajectories and reasoning traces from early to later rounds, and quantify each experiment using the cooperation ratio.

For all LLM inference, we set the temperature to 0.7 and the maximum output length to 2,000 tokens, and allowed each interaction to continue with probability 0.99 after every round, up to a maximum of 500 rounds. We varied the accessible interaction-history length over {0, 1, 2, 3, 5, 10, 20, 40, 80}, and repeated each setting for three times. All experiments were conducted using open-source models accessed through the Cloudflare Workers AI platform’s API111https://developers.cloudflare.com/workers-ai/.

4Mechanisms of the Memory Curse: How Expanded Recall Erodes Trust

Based on the experimental results, we identified two behavioral patterns across LLMs and games (Figure2and Appendix Table1). The first pattern is consistent cooperation, observed for Llama-3.3-70B, Qwen2.5-Coder-32B across multiple games, as well as for Gemma-3-12B, GPT-OSS-120B, Mistral-7B, and Llama-4-Scout-17B in the Prisoner’s Dilemma. This long-term cooperative behavior appears to primarily arise from two factors: (1) an intrinsic tendency toward cooperation in certain models, and (2) a sufficient understanding and forward-looking, through reasoning, of the long-term benefits of cooperation in specific games, regardless of memory content (sample reasoning patterns in AppendixB).

The second pattern is memory-bounded behavior. In this case, LLM agents tend to defect at memory length 0 (see Appendix Table1for details), achieve their highest cooperation at short memory length (typicallyH​L≤5HL\leq 5), and then show decreasing cooperation as memory length further increases (Figure2). This pattern suggests that, under explicit reasoning, LLM agents rely on a memory band of usable history: too little history promotes betrayal forgiveness, whereas too much history appears to slow trust recovery.

To unpack the mechanisms behind this memory-bound strategy, the following subsections systematically deconstruct the memory curse. We first detail its behavioral trajectory (Section4.1) and uncover its cognitive basis, validating the protective role of forward-looking reasoning via a targeted fine-tuning intervention (Section4.2). We then isolate the dynamics of trust erosion through semantic tracking (Section4.3), asymmetric interactions (Section4.4), and memory sanitization (Section4.5). Finally, a no-reasoning ablation reveals that without explicit deliberation, cooperation is generally less sensitive to increasing history length and declines more slowly (Section4.6).

Figure 2:Cooperation rate across four social dilemmas as history length (H​LHL) expands. The x-axis (non-linear scale) begins atH​L=2HL=2to focus on the strategic regime of repeated interaction. Each panel reports the mean cooperation rate, with shaded bands denoting standard deviation.### 4.1From Zero Memory to the Memory Curse

A core tenet of reciprocity is that cooperation cannot be strategically sustained without memory. Consistent with this classical game-theoretic intuition, when agents lack prior interaction history (H​L=0HL{=}0), their behavior is largely non-reciprocal. Confined to a static, one-shot reasoning paradigm, models prioritize immediate protection against exploitation, heavily defaulting to the Nash equilibrium of mutual defection (e.g., near-zero cooperation in the Public Goods and Trust Games; see Appendix Table1for full zero-memory baselines). However, granting a minimal memory window (H​L=2HL{=}2) fundamentally alters the interaction dynamic. It allows agents to interpret recent actions as evidence of intent, serving as a catalyst for trust repair and reactive strategies (e.g. Tit-for-Tat), which sharply increases cooperation across most models.

The most profound observation, however, emerges as history length expands beyond this optimal short window. As shown in Figure2, rather than stabilizing trust, the continuous expansion of passive historical memory degrades cooperation, producing a counter-intuitive “Memory Curse”. This behavioral deterioration is severe and materially impacts long-run welfare: for example, in the Trust Game, Gemma-3-12B’s cooperation rate declines from 51.2% atH​L=2HL{=}2to 9.5% atH​L=80HL{=}80, dragging its cumulative reward down from 8.59 to 5.19 (Appendix Tables2–5).

When forced to explicitly reason over extended contexts, LLMs appear to suffer from “historical overfitting.” In a long-context setting, an occasional noisy action (ϵ\epsilon) inevitably triggers a retaliatory defection. Because the history window is expansive, the textual record of this defensive response persists in the prompt for many rounds. From a language modeling perspective, this crowds the context window with defection tokens, skewing the local in-context distribution and gradually hardening the interaction into a fixed negative pattern that overpowers the model’s intrinsic cooperative prior and blocks later trust recovery (sample reasoning traces in AppendixC).

The empirical decay is striking across both models and games: GPT-OSS-20B in the Prisoner’s Dilemma decreases from 92.1% (H​L=2HL{=}2) to a mere 20.6% (H​L=80HL{=}80); similarly, Llama-4-Scout-17B in the Public Goods Game collapses from 82.6% to 45.8%. The standard deviations (±\pm) reported in Appendix Table1provide further mechanical insight: atH​L=2HL{=}2, models generally maintain low variance, tightly bounding their cooperative policies. But asH​L→80HL{\to}80, variance explodes (e.g.,±24.0%\pm 24.0\%for Llama-4-Scout-17B). This indicates that longer memories amplify the butterfly effect of noisy early interactions, trapping agents in path-dependent retaliation cycles that make the behavioral regime highly rigid within a single episode, yet wildly unstable across different initialization seeds.

(a)Memory Immune vs. Memory Cursed. (b)Semantic shift in CoT reasoning.

Figure 3:(a)Memory Immune settings. We also observe that the certain models in certain games always show cooperation behavior with larger than 95% cooperation rate across different game-model settings. This plot shows the lexical analysis of the models’ reasoning traces reveals a clear cognitive basis for this divergence: immune models consistently sustain a significantly higher ratio of forward-looking reasoning pattern compared to cursed models (e.g., maintaining a mean ratio of 0.504 atH​L=80HL{=}80). See AppendixDfor details.(b)Comprehensive analysis of model behavior: (a-left) The frequency of Cooperation Words collapses across HL steps. (a-right) The Paranoia Ratio increases as history expands.

4.2Cognitive Divergence and Causal Verification of Strategic Intent

While expanding memory length generally degrades cooperation, we observed that this curse is not entirely universal. Among our 28 evaluated model-game settings, 10 maintained≥95%\geq 95\%cooperation across all history lengths (classified asMemory Immune), while the remaining 18 exhibited severe decay (classified asMemory Cursed), as detailed in Appendix Table7. To understand this divergence, we conducted a large-scale lexical analysis of the reasoning traces. By calculating the ratio of forward-looking, long-term keywords against history-following, risk-averse terms (Figure3(a)), we established a metric for the agents’ strategic intent.

This analysis suggests a cognitive-linguistic correlate of the divergence: while expanding the memory length (e.g.,H​L=2HL{=}2toH​L=80HL{=}80) generally suppresses forward-looking reasoning across the board, Memory Immune settings consistently sustain a significantly higher baseline of this proactive cognitive state. For instance, atH​L=80HL{=}80, immune models retained a mean forward-looking ratio of 0.504, whereas cursed models plummet to 0.340. This pattern suggests that immune settings do not simply ignore history; rather, their reasoning traces continue to contain more forward-looking language even under expanded memory. See AppendixDfor more detailed analysis.

However, the strong correlation between vocabularies and behavior raises a critical epistemological question: is forward-looking reasoning merely a byproduct of a capable model, or does it play an active role in sustaining cooperation under expanded memory? To investigate this, we curated a specialized training corpus of Public Goods Game (PG) reasoning traces. During this curation process, we applied a rigorous two-stage filter to select traces enriched exclusively with forward-looking, long-term deliberation. Strikingly, we observed that among traces filtered strictly for this cognitive style, 98% organically culminated in a cooperative action (with only 2% defaulting to defection). While this confirms a massive correlational link, validating this mechanism requires an active intervention.

We emphasize that our subsequent fine-tuning experiment is not proposed as a scalable engineering “solution” to the memory curse, but rather as an interventional probe of this hypothesis. Following the behavioral priming methodology ofGandhiet al.(2025), we trained a LoRA adapter on Mistral-7B (a model previously identified as universally Memory Cursed across all the four games) using this highly forward-looking PG corpus. Critically, we filtered the training data exclusively on the semantic reasoning style and never on the chosen action. This design reduces, but does not eliminate, the possibility of trivial action-label learning, because the selected reasoning style is naturally correlated with cooperative outcomes. We optimized the model via a weighted SFT loss (details in AppendixI).

As shown in Table1, the intervention successfully inverts the behavioral regime. AtH​L=80HL{=}80(where the memory curse is most severe), cooperation rates surge by +14.7 to +79.3 percentage points across all four games. Consequently, the fine-tuned model transitions from being uniformly Memory Cursed to maintaining robust cooperation, achieving near 100% cooperation in PG, TG, and PD, and dramatically improving in TD.

Crucially, this robust zero-shot transfer supports the interpretation that the adapter changes a transferable reasoning tendency rather than only memorizing game-specific action labels. Although the model was fine-tuned exclusively on reasoning traces from the Public Goods Game (PG), it exhibits remarkable generalization to the other three structurally distinct games. For instance, while the cooperative action in the PG training corpus is strictly tokenized asA0A_{0}, the model successfully drives zero-shot cooperation in TD (which requiresA3A_{3}, the highest claim) and PD (where action labels “Option A/B” never appear in training). This transfer pattern makes a purely surface-level action-token memorization explanation less likely, and supports the interpretation that the adapter induces a transferable forward-looking reasoning tendency. Overall, the intervention provides evidence that the memory curse is partly driven by a reasoning-style vulnerability to accumulated historical evidence, which can be mitigated by explicitly anchoring the agent’s reasoning toward long-term cooperation.

To ensure that the fine-tuning process did not compromise the model’s general reasoning and knowledge base, we evaluated both the base and LoRA fine-tuned Mistral-7B models across several benchmarks, including GSM8K, TriviaQA, HumanEval, and MBPP. The results indicate that the fine-tuned model achieved a slight improvement in mathematical reasoning (+2.3% on GSM8K) while maintaining comparable performance in general knowledge and coding tasks, confirming the stability of our fine-tuning approach without significant catastrophic forgetting (detailed results are provided in AppendixI.3).

Table 1:Cooperation rate (%)±\pmstd for base Mistral-7B vs forward-looking-fine-tuned Mistral-7B (ours). FT was trained only on PG traces; transfer to the other three games is zero-shot.GameModelHL=2HL=5HL=10HL=20HL=40HL=80PDMistral-7B (base)96.9±0.993.6±1.495.5±2.294.3±3.591.3±2.585.3±2.9+ Forward FT (ours)100.0±0.1100.0±0.0100.0±0.0100.0±0.0100.0±0.0100.0±0.1PGMistral-7B (base)74.9±2.264.6±1.060.1±1.255.3±1.655.1±2.650.3±3.1+ Forward FT (ours)99.9±0.1100.0±0.0100.0±0.0100.0±0.0100.0±0.099.9±0.1TDMistral-7B (base)25.2±0.724.5±1.421.5±1.118.8±1.616.9±0.816.6±0.3+ Forward FT (ours)∗71.0±3.181.7±24.998.2±1.674.4±45.286.4±34.195.9±2.6TGMistral-7B (base)37.8±0.940.2±0.839.3±0.337.6±0.438.3±1.034.8±0.2+ Forward FT (ours)92.1±0.496.9±2.597.7±0.699.4±0.799.9±0.2100.0±0.1∗TD HL=5/20/40 are bimodal (12-25% of seeds collapse to race-to-defect; n=8 seeds reported).

4.3Semantic Analysis of the Memory Curse: The Erosion of Cooperative Intent

While the previous section explains how immune models resist historical noise, we now investigate the reasoning pattern associated with the memory curse. Specifically, as the accessible history length (H​LHL) expands, how exactly does an agent’s reasoning degrade? Are the models actively becoming more vindictive, or are they passively losing their capacity to trust?

Using the same semantic analysis framework on the chain-of-thought logs, we classified the intent of words intoParanoia(e.g., betray, risk) andCooperation(e.g., trust, sustain) (Figure3(b)); methodology detailed in AppendixE. Our analysis shows that the absolute frequency of defensive paranoia remains roughly the same across history lengths. However, the behavioral collapse is better explained by reduced cooperative language than by a large increase in defensive language (Figure3(b)left). At bounded recall (H​L=2HL{=}2), agents actively plan for mutual benefit. However, as historical noise accumulates (H​L=80HL{=}80), cooperative reasoning systematically collapses (e.g., plummeting by 57% in GPT-OSS-20B).

Consequently, the relativeParanoia Ratioincreases as history lengthens (Figure3(b)right). Extended context crowds out the agents’ capacity to envision mutual benefit. While larger and more capable models (e.g., Llama-3.3-70B) exhibit cognitive resilience against this drift, susceptible models show fewer forward-looking cooperative rationales and are more likely to settle into pessimistic strategies.

4.4The Tragedy of Overthinking: Asymmetric Memory in Social Dilemmas

Figure 4:Asymmetric memory evaluation across the Trust Game and Public Goods Game.(a)Trust Game cooperation rates across symmetric and asymmetricH​LHLconfigurations.(b)Public Goods Game overall group welfare under varying ratios of short- vs. long-memory agents.(c)Per-player cooperation breakdown in the adversarial majority setting (oneH​L=2HL{=}2agent vs. twoH​L=80HL{=}80agents).To isolate the behavioral impact of the Memory Curse, we conducted a heterogeneous evaluation where agents with bounded recall (H​L=2HL{=}2, “forgivers”) interact directly with agents possessing extended history (H​L=80HL{=}80, “grudge-holders”). This asymmetric setting allows us to observe whether the breakdown of trust is a systemic environmental failure or driven by the specific cognitive pathology of long-memory agents.

Our evaluation across the 2-player Trust Game and the 3-player Public Goods game reveals a consistent, cross-model “Tragedy of Overthinking” (see Figure4for the visual summary and AppendixFfor the complete quantitative breakdown):

1. The Grudge-Holder as the “Toxic Component” (Trust Game).In the exact same interactive environment, theH​L=80HL{=}80agent acts as the primary bottleneck for trust. Figure4a demonstrates that the asymmetric pair consistently falls below the symmetricH​L=2HL{=}2baseline. More importantly, the individual cooperation rate of the grudge-holder is significantly lower than their forgiving partner. For instance, Llama-4-Scout-17B exhibits a massive +28pp individual gap: the long-memory agent actively chooses defection while the short-memory agent futilely attempts to reciprocate trust.

2. Systemic Contagion of Distrust (3-Player Public Goods).The presence of even a single grudge-holder induces social contagion, dragging forgiving partners into a punishment cycle. As shown in Figure4b, systematically replacingH​L=2HL{=}2agents withH​L=80HL{=}80agents degrades group welfare. For example, GPT-OSS-20B crashes from a highly cooperative state in a symmetricH​L=2HL{=}2society down to a mere fraction of its potential when mixed with grudge-holders.

3. Cognitive Resilience Under Majority Pressure.Crucially, bounded recall serves as a robust functional forgiveness mechanism. Figure4c illustrates that even when structurally outnumbered by two grudge-holders, the loneH​L=2HL{=}2forgiver preserves its cooperative intent, maintaining significantly higher individual cooperation (e.g., a +33pp gap over its adversarial peers in GPT-OSS-20B).

4.5Memory Content vs. Context Length: Sanitization Results

Figure 5:Evidence that the memory-content sensitivity is widespread but can be overridden, and driven by memory content rather than length.(a)Defection mention rate versus cooperation rate atH​L=80HL{=}80. Some (mostly relatively stronger) models (Llama-3.3-70B, Qwen2.5-Coder-32B, Qwen3-30B) reference defection in up to∼90%{\sim}90\%of their reasoning traces yet sustain high cooperation, demonstrating that they are not immune to the memory curse but actively override it through forward-looking reasoning. In contrast, some other models (including relatively weaker ones like GPT-OSS-20B and Mistral-7B, and also GPT-OSS-120B) collapse, which could be due to lacking the reasoning depth to override.(b)Memory sanitization in the Trust Game atH​L=80HL{=}80. Replacing 78 of the 80 history rounds with synthetic cooperative records (sanitized,X=2X{=}2real rounds) restores cooperation substantially across all five models.Is the memory curse a fundamental architectural limitation of long-context inference (length), or a behavioral artifact of accumulated negative evidence (content)? To isolate this, we conduct a memory sanitization experiment in the Trust Game atH​L=80HL{=}80(Figure5). We replace80−X80-Xof the visible rounds with synthetic mutual-cooperation records, leaving onlyXXrecent real rounds intact. Crucially, because the prompt window remains fixed at 80 rounds, any performance shift can only be attributed to the altered content.

As Figure5b shows, replacing defection records with cooperative ones dramatically restores cooperation. For most models, cooperation recovers significantly fromX=80X{=}80baseline toX=2X{=}2. The recovery monotonically decreases as more real history is exposed (full sweep in AppendixH). Furthermore, lexical analysis (Figure5a) confirms that the curse is universal: all models (even Memory Immune ones) highly perceive defection signals in their reasoning traces. The divergence lies in cognitive override: many stronger models actively push back against the negative pull of historical evidence via forward-looking reasoning, while some weaker models collapse. Together, these results confirm that the memory curse is a content-driven behavioral susceptibility rather than a context-length limitation.

4.6Ablation Study: Explicit Reasoning Amplifies the Curse

Is the memory curse driven passively by memory length or actively by explicit reasoning? We conducted an ablation study where agents output only their final decision without intermediate CoT (full unreasoned baselines in Appendix Tables2–6). Comparing the two settings reveals that removing explicit CoT generally mitigates the memory curse. When isolating the specific game that pushes each model to its strategic limit (detailed in AppendixG), the destructive nature of explicit reasoning becomes stark. For instance, atH​L=80HL{=}80, Llama-3.3-70B cooperates perfectly (100.0%) intuitively without reasoning. However, when forced to generate a CoT, its cooperation collapses to 6.9%—a devastating−93.1-93.1percentage point penalty for deliberation. Similar maximum deliberation penalties are observed for Qwen2.5-Coder-32B (−77.2-77.2pp) and Gemma-3-12B (−64.7-64.7pp). This suggests that explicit reasoning can amplify the memory curse, and in some settings can turn an otherwise cooperative policy into a defecting one: CoT traces often devote additional space to enumerating past defections, which may make retaliatory decisions easier to justify.

5Conclusion

In this work, we challenged the prevailing assumption that expanding an LLM agent’s context window naturally enhances strategic cooperation. Through large-scale evaluations across diverse social dilemmas, we identified a pervasive “memory curse”: extended interaction histories frequently trap agents in retaliatory cycles. Through memory sanitization, reasoning ablation, and a targeted fine-tuning intervention, we isolated the underlying mechanism. We demonstrate that this behavioral collapse is driven primarily by a cognitive vulnerability to accumulated negative content, rather than a simple architectural limitation of long-context processing, which is paradoxically amplified by explicit Chain-of-Thought deliberation. Crucially, explicitly reshaping a susceptible agent’s cognitive prior toward forward-looking reasoning mitigates this decay and transfers zero-shot across distinct environments. This confirms that in long-horizon interactions, raw memory expansion can easily become a liability; transforming it into a strategic asset requires complementary mechanisms (e.g., a forward-looking reasoning style) that actively preserve the possibility of future trust.

Our findings open several crucial avenues for future research. First, while our intervention relied on static fine-tuning, future work should explore dynamic memory curation mechanisms—such as selective forgetting, strategic summarization, or specialized retrieval-augmented generation (RAG)—allowing agents to autonomously filter historical noise during inference. Second, scaling these interactions to open-ended,NN-player societies with heterogeneous LLM architectures will clarify how divergent cognitive priors influence emergent societal norms and systemic contagion. Ultimately, as AI agents are increasingly deployed in long-horizon collaborative settings, equipping them with the cognitive capacity to “forgive” and strategize beyond the immediate past will be just as critical as expanding their raw memory limits.

Acknowledgment

Jiayuan Liu and Vincent Conitzer thank the Cooperative AI Foundation, Macroscopic Ventures (formerly Polaris Ventures / the Center for Emerging Risk Research) and Jaan Tallinn’s donor-advised fund at Founders Pledge for financial support. Shiyi Du and Carl Kingsford thank the US National Science Foundation [III-2232121] and the US National Institutes of Health [R01HG012470] for partial support. Shiyi Du is partially supported by the SoftBank Group–Arm Fellowship. Jiayuan Liu, Tianqin Li, Shiyi Du, and Xin Luo thank the Intelligence Cubed Fellowship for partial computational support in the form of LLM API credits. Conflict of Interest: Carl Kingsford is a co-founder of Ellumigen, Inc.

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Appendix

Appendix Table 1:Average Cooperation Rate (%)±\pmStandard Deviation across four repeated social dilemmas, different models (with CoT reasoning), and various history lengths.Social dilemmaModelHistory length (HL)0†123510204080Prisoner’sDilemmaGemma-3-12B2.7±\pm0.6100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-20B47.4±\pm1.399.1±\pm0.592.1±\pm1.884.9±\pm7.136.2±\pm11.423.4±\pm2.216.7±\pm5.212.3±\pm2.320.6±\pm15.1Llama-4-Scout-17B54.4±\pm0.7100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Mistral-7B81.7±\pm0.7100.0±\pm0.096.9±\pm0.996.9±\pm0.893.6±\pm1.495.5±\pm2.294.3±\pm3.591.3±\pm2.585.3±\pm2.9Llama-3.3-70B36.0±\pm1.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.099.9±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-120B42.3±\pm0.6100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Qwen2.5-Coder-32B37.2±\pm0.6100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Public GoodsGameGemma-3-12B8.2±\pm0.50.0±\pm0.074.0±\pm3.371.0±\pm1.975.4±\pm4.675.0±\pm7.163.1±\pm6.859.8±\pm9.553.0±\pm5.9GPT-OSS-20B4.2±\pm0.446.6±\pm0.743.5±\pm0.841.8±\pm1.228.8±\pm1.720.0±\pm0.413.8±\pm2.17.2±\pm0.75.2±\pm0.4Llama-4-Scout-17B3.8±\pm0.290.0±\pm0.782.6±\pm0.275.8±\pm2.371.3±\pm2.563.1±\pm3.364.5±\pm2.457.1±\pm6.045.8±\pm24.0Mistral-7B65.6±\pm1.0100.0±\pm0.074.9±\pm2.271.0±\pm0.664.6±\pm1.060.1±\pm1.255.3±\pm1.655.1±\pm2.650.3±\pm3.1Llama-3.3-70B2.9±\pm0.5100.0±\pm0.099.8±\pm0.2100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-120B0.0±\pm0.072.5±\pm0.275.4±\pm2.777.0±\pm2.550.4±\pm11.523.1±\pm4.413.1±\pm2.37.3±\pm3.24.0±\pm0.5Qwen2.5-Coder-32B11.2±\pm0.4100.0±\pm0.099.2±\pm0.197.9±\pm0.398.3±\pm0.697.5±\pm1.098.0±\pm0.697.3±\pm1.297.9±\pm1.5Traveler’sDilemmaGemma-3-12B19.0±\pm0.5100.0±\pm0.070.3±\pm6.867.1±\pm22.262.4±\pm26.051.2±\pm18.768.6±\pm41.463.4±\pm42.435.3±\pm15.4GPT-OSS-20B20.5±\pm0.642.2±\pm2.042.0±\pm2.833.3±\pm4.08.6±\pm1.64.8±\pm0.94.5±\pm0.42.8±\pm0.32.7±\pm1.2Llama-4-Scout-17B35.2±\pm2.20.4±\pm0.299.2±\pm1.195.9±\pm3.398.5±\pm1.697.4±\pm3.3100.0±\pm0.095.6±\pm6.2100.0±\pm0.0Mistral-7B17.9±\pm1.312.0±\pm0.525.2±\pm0.722.3±\pm1.324.5±\pm1.421.5±\pm1.118.8±\pm1.616.9±\pm0.816.6±\pm0.3Llama-3.3-70B96.0±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.099.9±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-120B2.1±\pm0.688.8±\pm9.292.8±\pm7.790.3±\pm13.278.4±\pm14.1100.0±\pm0.066.6±\pm42.934.2±\pm46.612.6±\pm15.4Qwen2.5-Coder-32B25.9±\pm2.498.3±\pm0.188.9±\pm0.664.0±\pm17.450.2±\pm36.934.7±\pm26.561.9±\pm15.79.6±\pm1.08.0±\pm0.5Trust GameGemma-3-12B1.4±\pm0.30.1±\pm0.151.2±\pm3.146.2±\pm0.944.9±\pm4.631.8±\pm2.020.4±\pm2.611.8±\pm1.79.5±\pm0.9GPT-OSS-20B2.9±\pm0.115.9±\pm1.528.7±\pm0.321.9±\pm3.114.8±\pm0.58.6±\pm0.76.3±\pm0.43.7±\pm0.73.4±\pm0.6Llama-4-Scout-17B1.6±\pm0.338.7±\pm2.645.0±\pm1.034.7±\pm1.024.9±\pm5.421.3±\pm3.410.2±\pm3.73.6±\pm0.22.2±\pm0.5Mistral-7B14.5±\pm0.721.8±\pm1.437.8±\pm0.939.2±\pm0.440.2±\pm0.839.3±\pm0.337.6±\pm0.438.3±\pm1.034.8±\pm0.2Llama-3.3-70B0.2±\pm0.2100.0±\pm0.050.8±\pm2.450.8±\pm14.647.0±\pm5.032.8±\pm9.845.7±\pm5.98.3±\pm3.96.9±\pm4.4GPT-OSS-120B3.4±\pm0.282.8±\pm4.092.7±\pm2.199.3±\pm0.398.7±\pm1.357.6±\pm15.414.8±\pm4.714.4±\pm7.87.3±\pm4.7Qwen2.5-Coder-32B5.3±\pm0.3100.0±\pm0.098.0±\pm1.894.1±\pm1.592.0±\pm3.990.2±\pm7.699.2±\pm0.399.1±\pm0.298.3±\pm0.7†AtH​L=0HL{=}0, the 500 rounds are effectively independent one-shot games. The standard deviation in this column is thus computed across these independent rounds rather than across different random interaction seeds.Same for other tables withH​L=0HL{=}0data.

Appendix Table 2:Discounted Reward (R​e​w​a​r​d=∑t=1Tδt−1⋅Rt∑t=1Tδt−1Reward=\frac{\sum_{t=1}^{T}\delta^{t-1}\cdot R_{t}}{\sum_{t=1}^{T}\delta^{t-1}}withδ=0.99\delta=0.99) averaged across three runs for No Reasoning (NR) and Reasoning (R). Results for Prisoner’s Dilemma and Public Goods Game are shown below. Values are reported as mean±\pmstandard deviation.Social dilemmaModelSettingHistory length (HL)0123510204080Prisoner’sDilemmaGemma-3-12BNR199.52±\pm0.68200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R100.37±\pm0.43200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00GPT-OSS-20BNR178.22±\pm1.14198.35±\pm1.41196.03±\pm3.20192.86±\pm2.88177.45±\pm16.65147.67±\pm19.67164.83±\pm10.35136.14±\pm28.69132.04±\pm16.97R121.82±\pm0.95199.64±\pm0.29192.86±\pm1.91186.88±\pm8.48142.60±\pm25.90120.38±\pm12.55128.72±\pm11.94115.40±\pm9.98134.46±\pm28.35GPT-OSS-120BNR187.61±\pm1.98200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R118.77±\pm0.86200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00Llama-3.3-70BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R113.85±\pm2.10200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00199.99±\pm0.01200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00Llama-4-Scout-17BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00199.75±\pm0.35200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R129.59±\pm1.29200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00Mistral-7BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00192.84±\pm3.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R166.55±\pm4.23200.00±\pm0.00193.21±\pm4.25193.70±\pm1.94189.61±\pm1.66185.93±\pm7.29186.50±\pm6.57177.05±\pm2.46176.36±\pm12.01Qwen2.5-Coder-32BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R111.33±\pm1.22200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00199.96±\pm0.06Public GoodsGameGemma-3-12BNR1.00±\pm0.001.00±\pm0.001.00±\pm0.001.38±\pm0.011.00±\pm0.001.00±\pm0.001.00±\pm0.001.00±\pm0.001.00±\pm0.00R1.04±\pm0.001.00±\pm0.001.35±\pm0.021.38±\pm0.021.35±\pm0.021.36±\pm0.011.30±\pm0.051.30±\pm0.051.29±\pm0.05GPT-OSS-20BNR1.08±\pm0.001.22±\pm0.011.25±\pm0.031.26±\pm0.011.27±\pm0.031.25±\pm0.001.25±\pm0.061.13±\pm0.051.16±\pm0.07R1.02±\pm0.001.24±\pm0.001.22±\pm0.011.21±\pm0.001.16±\pm0.011.10±\pm0.001.08±\pm0.011.05±\pm0.011.05±\pm0.01GPT-OSS-120BNR1.00±\pm0.001.42±\pm0.021.40±\pm0.021.34±\pm0.041.34±\pm0.021.26±\pm0.021.17±\pm0.071.09±\pm0.021.11±\pm0.01R1.00±\pm0.001.36±\pm0.021.40±\pm0.021.39±\pm0.011.27±\pm0.071.14±\pm0.021.10±\pm0.031.08±\pm0.061.05±\pm0.01Llama-3.3-70BNR1.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00R1.01±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00Llama-4-Scout-17BNR1.50±\pm0.001.48±\pm0.011.50±\pm0.011.40±\pm0.011.45±\pm0.001.46±\pm0.001.41±\pm0.001.36±\pm0.021.41±\pm0.02R1.02±\pm0.001.46±\pm0.001.42±\pm0.011.39±\pm0.011.35±\pm0.021.33±\pm0.021.31±\pm0.041.27±\pm0.081.32±\pm0.16Mistral-7BNR1.47±\pm0.011.50±\pm0.001.50±\pm0.001.37±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00R1.33±\pm0.011.50±\pm0.001.37±\pm0.021.34±\pm0.011.32±\pm0.011.31±\pm0.011.29±\pm0.011.28±\pm0.021.27±\pm0.02Qwen2.5-Coder-32BNR1.17±\pm0.011.50±\pm0.001.50±\pm0.011.49±\pm0.001.50±\pm0.001.49±\pm0.011.50±\pm0.001.50±\pm0.001.50±\pm0.00R1.06±\pm0.011.50±\pm0.001.50±\pm0.001.49±\pm0.001.49±\pm0.001.49±\pm0.001.49±\pm0.011.49±\pm0.001.49±\pm0.01

Appendix Table 3:Discounted Reward (R​e​w​a​r​d=∑t=1Tδt−1⋅Rt∑t=1Tδt−1Reward=\frac{\sum_{t=1}^{T}\delta^{t-1}\cdot R_{t}}{\sum_{t=1}^{T}\delta^{t-1}}withδ=0.99\delta=0.99) averaged across three runs for No Reasoning (NR) and Reasoning (R) settings, continued for Traveler’s Dilemma and Trust Game. Values are reported as mean±\pmstandard deviation.Social dilemmaModelSettingHistory length (HL)0123510204080Traveler’sDilemmaGemma-3-12BNR5.00±\pm0.004.99±\pm0.025.00±\pm0.004.35±\pm0.135.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.00R3.76±\pm0.025.00±\pm0.004.32±\pm0.254.46±\pm0.213.53±\pm0.483.02±\pm0.444.18±\pm0.973.98±\pm0.882.80±\pm0.11GPT-OSS-20BNR3.32±\pm0.504.55±\pm0.243.94±\pm0.363.79±\pm0.292.94±\pm0.923.17±\pm0.843.18±\pm0.763.29±\pm0.413.64±\pm0.37R2.39±\pm0.053.26±\pm0.313.55±\pm0.133.26±\pm0.282.25±\pm0.102.18±\pm0.092.32±\pm0.102.31±\pm0.252.50±\pm0.52GPT-OSS-120BNR2.01±\pm0.004.51±\pm0.084.55±\pm0.274.54±\pm0.274.16±\pm1.195.00±\pm0.004.37±\pm0.715.00±\pm0.002.98±\pm1.14R2.05±\pm0.014.71±\pm0.284.28±\pm0.724.23±\pm1.043.83±\pm1.065.00±\pm0.003.94±\pm1.003.08±\pm1.363.11±\pm1.02Llama-3.3-70BNR5.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.00R4.82±\pm0.025.00±\pm0.005.00±\pm0.005.00±\pm0.004.99±\pm0.015.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.00Llama-4-Scout-17BNR4.99±\pm0.014.00±\pm0.004.00±\pm0.024.98±\pm0.014.00±\pm0.004.04±\pm0.054.00±\pm0.004.00±\pm0.004.33±\pm0.47R4.06±\pm0.034.01±\pm0.014.94±\pm0.084.92±\pm0.044.82±\pm0.134.92±\pm0.085.00±\pm0.004.67±\pm0.474.75±\pm0.35Mistral-7BNR2.99±\pm0.012.90±\pm0.053.11±\pm0.073.07±\pm0.053.15±\pm0.033.14±\pm0.023.23±\pm0.053.08±\pm0.063.14±\pm0.04R3.22±\pm0.043.19±\pm0.063.06±\pm0.113.06±\pm0.023.17±\pm0.033.11±\pm0.093.06±\pm0.053.01±\pm0.013.09±\pm0.10Qwen2.5-Coder-32BNR4.23±\pm0.004.22±\pm0.064.81±\pm0.084.68±\pm0.074.86±\pm0.124.57±\pm0.254.72±\pm0.064.56±\pm0.064.47±\pm0.09R3.97±\pm0.054.89±\pm0.014.76±\pm0.144.21±\pm0.164.39±\pm0.444.18±\pm0.204.10±\pm0.183.97±\pm0.023.96±\pm0.02TrustGameGemma-3-12BNR4.00±\pm0.004.00±\pm0.006.10±\pm0.888.39±\pm0.164.20±\pm0.094.11±\pm0.084.11±\pm0.034.07±\pm0.004.07±\pm0.00R4.11±\pm0.024.05±\pm0.078.79±\pm0.238.19±\pm0.198.14±\pm0.227.40±\pm0.207.08±\pm0.226.17±\pm0.716.32±\pm0.35GPT-OSS-20BNR4.87±\pm0.277.56±\pm0.317.90±\pm0.108.15±\pm0.207.77±\pm0.147.54±\pm0.257.52±\pm0.487.41±\pm0.457.38±\pm0.30R4.37±\pm0.056.11±\pm0.157.15±\pm0.156.77±\pm0.365.80±\pm0.035.44±\pm0.075.05±\pm0.184.82±\pm0.184.76±\pm0.26GPT-OSS-120BNR4.15±\pm0.029.62±\pm0.169.91±\pm0.069.59±\pm0.048.49±\pm1.476.16±\pm0.365.53±\pm0.455.08±\pm0.714.38±\pm0.19R4.51±\pm0.058.76±\pm0.759.88±\pm0.109.98±\pm0.029.88±\pm0.127.79±\pm1.135.54±\pm0.576.79±\pm1.096.00±\pm1.12Llama-3.3-70BNR4.00±\pm0.0010.00±\pm0.0010.00±\pm0.008.91±\pm0.1210.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.00R4.03±\pm0.0310.00±\pm0.007.93±\pm0.258.30±\pm0.627.16±\pm0.516.57±\pm1.177.14±\pm0.225.74±\pm0.785.70±\pm0.97Llama-4-Scout-17BNR5.32±\pm0.2310.03±\pm0.108.39±\pm0.218.91±\pm0.037.06±\pm0.106.48±\pm0.095.98±\pm0.315.07±\pm0.175.37±\pm0.43R4.20±\pm0.038.14±\pm0.098.44±\pm0.137.84±\pm0.066.52±\pm0.316.20±\pm0.235.27±\pm0.254.75±\pm0.054.60±\pm0.12Mistral-7BNR4.11±\pm0.038.86±\pm0.107.46±\pm1.808.59±\pm0.054.51±\pm0.164.61±\pm0.106.54±\pm2.468.82±\pm1.677.81±\pm1.53R5.88±\pm0.346.18±\pm0.488.10±\pm0.108.10±\pm0.168.18±\pm0.078.17±\pm0.128.17±\pm0.078.28±\pm0.188.04±\pm0.04Qwen2.5-Coder-32BNR4.00±\pm0.0010.00±\pm0.0010.00±\pm0.009.98±\pm0.0110.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.00R4.81±\pm0.0610.00±\pm0.0010.01±\pm0.019.95±\pm0.149.83±\pm0.199.96±\pm0.0710.02±\pm0.0110.02±\pm0.0110.04±\pm0.03

Appendix Table 4:Cumulative Reward (undiscounted) averaged across three runs for No Reasoning(NR) and Reasoning (R). Results for Prisoner’s Dilemma and Public Goods Game are shown below. Values are reported as mean±\pmstandard deviation.Social dilemmaModelSettingHistory length (HL)0123510204080Prisoner’sDilemmaGemma-3-12BNR199.80±\pm0.28200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R100.13±\pm0.09200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00GPT-OSS-20BNR175.20±\pm1.30198.40±\pm1.61195.40±\pm4.29192.47±\pm3.49181.00±\pm13.85145.87±\pm10.55163.80±\pm12.72123.33±\pm27.91116.67±\pm7.41R121.40±\pm1.56198.73±\pm0.57189.07±\pm2.47181.40±\pm8.35127.93±\pm12.57114.13±\pm1.48108.93±\pm4.50105.07±\pm2.17113.80±\pm13.89GPT-OSS-120BNR187.80±\pm0.28200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R117.47±\pm0.81200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00Llama-3.3-70BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R113.73±\pm1.37200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00199.80±\pm0.28200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00Llama-4-Scout-17BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00199.87±\pm0.19200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R128.33±\pm0.25200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00Mistral-7BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00193.07±\pm0.50200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R166.75±\pm1.34200.00±\pm0.00194.00±\pm1.56194.00±\pm1.61187.73±\pm2.69191.80±\pm3.83189.53±\pm6.49183.67±\pm4.88173.40±\pm4.55Qwen2.5-Coder-32BNR200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00R113.17±\pm0.91200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00200.00±\pm0.00199.90±\pm0.14Public GoodsGameGemma-3-12BNR1.00±\pm0.001.00±\pm0.001.00±\pm0.001.39±\pm0.011.00±\pm0.001.00±\pm0.001.00±\pm0.001.00±\pm0.001.00±\pm0.00R1.04±\pm0.001.00±\pm0.001.37±\pm0.021.36±\pm0.011.38±\pm0.021.38±\pm0.041.32±\pm0.031.30±\pm0.051.26±\pm0.03GPT-OSS-20BNR1.08±\pm0.001.22±\pm0.001.25±\pm0.031.25±\pm0.001.26±\pm0.041.26±\pm0.001.24±\pm0.061.09±\pm0.011.07±\pm0.02R1.02±\pm0.001.23±\pm0.001.22±\pm0.001.21±\pm0.001.14±\pm0.011.10±\pm0.001.07±\pm0.011.04±\pm0.001.03±\pm0.00GPT-OSS-120BNR1.00±\pm0.001.43±\pm0.011.40±\pm0.011.34±\pm0.011.33±\pm0.011.26±\pm0.011.11±\pm0.041.04±\pm0.011.04±\pm0.01R1.00±\pm0.001.36±\pm0.001.38±\pm0.011.38±\pm0.011.25±\pm0.061.12±\pm0.021.07±\pm0.011.04±\pm0.021.02±\pm0.00Llama-3.3-70BNR1.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00R1.01±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00Llama-4-Scout-17BNR1.50±\pm0.001.48±\pm0.001.50±\pm0.001.41±\pm0.001.44±\pm0.001.44±\pm0.021.37±\pm0.021.34±\pm0.031.35±\pm0.03R1.02±\pm0.001.44±\pm0.001.41±\pm0.001.38±\pm0.011.36±\pm0.011.32±\pm0.021.32±\pm0.011.29±\pm0.031.23±\pm0.12Mistral-7BNR1.47±\pm0.001.50±\pm0.001.50±\pm0.001.37±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00R1.33±\pm0.001.50±\pm0.001.37±\pm0.011.35±\pm0.001.32±\pm0.001.30±\pm0.011.28±\pm0.011.28±\pm0.011.25±\pm0.02Qwen2.5-Coder-32BNR1.17±\pm0.001.50±\pm0.001.50±\pm0.001.49±\pm0.001.49±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.001.50±\pm0.00R1.06±\pm0.001.50±\pm0.001.50±\pm0.001.49±\pm0.001.49±\pm0.001.49±\pm0.011.49±\pm0.001.49±\pm0.011.49±\pm0.01

Appendix Table 5:Cumulative Reward (undiscounted) averaged across three runs for No Reasoning (NR) and Reasoning (R) settings, continued for Traveler’s Dilemma and Trust Game. Values are reported as mean±\pmstandard deviation.Social dilemmaModelSettingHistory length (HL)0123510204080Traveler’sDilemmaGemma-3-12BNR5.00±\pm0.004.99±\pm0.015.00±\pm0.004.38±\pm0.155.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.00R3.77±\pm0.015.00±\pm0.004.47±\pm0.114.39±\pm0.414.18±\pm0.623.87±\pm0.464.21±\pm1.074.03±\pm1.243.34±\pm0.42GPT-OSS-20BNR3.35±\pm0.534.50±\pm0.133.95±\pm0.343.87±\pm0.122.93±\pm0.943.03±\pm0.882.96±\pm0.743.02±\pm0.593.31±\pm0.54R2.35±\pm0.023.39±\pm0.113.53±\pm0.083.14±\pm0.172.16±\pm0.042.11±\pm0.012.12±\pm0.052.09±\pm0.072.17±\pm0.20GPT-OSS-120BNR2.01±\pm0.004.68±\pm0.054.33±\pm0.174.61±\pm0.084.23±\pm1.095.00±\pm0.003.93±\pm1.135.00±\pm0.012.49±\pm0.64R2.04±\pm0.004.64±\pm0.294.77±\pm0.254.70±\pm0.424.32±\pm0.445.00±\pm0.003.99±\pm1.313.02±\pm1.402.43±\pm0.49Llama-3.3-70BNR5.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.00R4.82±\pm0.015.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.005.00±\pm0.00Llama-4-Scout-17BNR4.99±\pm0.004.00±\pm0.004.00±\pm0.004.99±\pm0.004.00±\pm0.004.02±\pm0.014.00±\pm0.004.00±\pm0.004.33±\pm0.47R4.07±\pm0.024.00±\pm0.004.97±\pm0.024.94±\pm0.054.96±\pm0.034.98±\pm0.025.00±\pm0.004.68±\pm0.454.91±\pm0.13Mistral-7BNR3.00±\pm0.002.93±\pm0.053.12±\pm0.023.12±\pm0.063.17±\pm0.053.16±\pm0.023.30±\pm0.033.12±\pm0.053.15±\pm0.09R3.22±\pm0.023.21±\pm0.033.10±\pm0.043.07±\pm0.013.16±\pm0.023.09±\pm0.043.04±\pm0.033.05±\pm0.023.09±\pm0.01Qwen2.5-Coder-32BNR4.21±\pm0.014.23±\pm0.064.96±\pm0.024.70±\pm0.054.97±\pm0.034.86±\pm0.104.93±\pm0.024.89±\pm0.024.85±\pm0.04R3.97±\pm0.034.98±\pm0.004.85±\pm0.014.58±\pm0.214.42±\pm0.434.22±\pm0.314.54±\pm0.193.95±\pm0.033.97±\pm0.01TrustGameGemma-3-12BNR4.00±\pm0.004.01±\pm0.004.80±\pm0.528.60±\pm0.134.04±\pm0.024.02±\pm0.024.02±\pm0.014.01±\pm0.004.01±\pm0.00R4.19±\pm0.044.01±\pm0.018.59±\pm0.158.17±\pm0.128.12±\pm0.147.34±\pm0.126.36±\pm0.275.49±\pm0.195.19±\pm0.13GPT-OSS-20BNR4.84±\pm0.117.55±\pm0.168.01±\pm0.048.17±\pm0.087.81±\pm0.167.41±\pm0.087.22±\pm0.356.97±\pm0.366.50±\pm0.15R4.39±\pm0.036.01±\pm0.137.23±\pm0.066.51±\pm0.185.75±\pm0.025.10±\pm0.044.80±\pm0.054.49±\pm0.064.44±\pm0.06GPT-OSS-120BNR4.15±\pm0.019.71±\pm0.069.74±\pm0.109.63±\pm0.029.11±\pm0.755.96±\pm0.334.89±\pm0.194.81±\pm0.594.19±\pm0.07R4.45±\pm0.019.35±\pm0.209.78±\pm0.069.99±\pm0.009.95±\pm0.068.10±\pm0.655.47±\pm0.275.44±\pm0.714.75±\pm0.36Llama-3.3-70BNR4.00±\pm0.0010.00±\pm0.0010.00±\pm0.008.82±\pm0.0410.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.00R4.02±\pm0.0210.00±\pm0.008.20±\pm0.087.88±\pm0.717.62±\pm0.176.61±\pm0.517.20±\pm0.304.93±\pm0.324.66±\pm0.26Llama-4-Scout-17BNR5.37±\pm0.0310.00±\pm0.098.38±\pm0.108.93±\pm0.117.15±\pm0.036.50±\pm0.015.95±\pm0.124.88±\pm0.055.30±\pm0.13R4.23±\pm0.058.05±\pm0.118.37±\pm0.117.70±\pm0.016.66±\pm0.406.25±\pm0.175.25±\pm0.294.49±\pm0.024.29±\pm0.06Mistral-7BNR4.14±\pm0.038.96±\pm0.098.08±\pm1.488.53±\pm0.054.38±\pm0.124.19±\pm0.016.23±\pm2.678.67±\pm1.887.50±\pm1.89R5.84±\pm0.166.44±\pm0.108.07±\pm0.048.15±\pm0.088.17±\pm0.108.17±\pm0.038.13±\pm0.038.23±\pm0.117.96±\pm0.12Qwen2.5-Coder-32BNR4.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.0110.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.0010.00±\pm0.00R4.72±\pm0.0410.00±\pm0.0010.00±\pm0.019.96±\pm0.059.85±\pm0.119.77±\pm0.2810.02±\pm0.0110.02±\pm0.0010.03±\pm0.01

Appendix Table 6:Average cooperation rate (%, mean±\pmstandard deviation) across four distinct social dilemmas for all models under theno-reasoningsetting.Social dilemmaModelHistory length (HL)0123510204080Prisoner’sDilemmaGemma-3-12B99.9±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-20B87.0±\pm0.799.1±\pm0.996.8±\pm3.095.4±\pm2.085.4±\pm10.758.9±\pm8.371.4±\pm10.630.5±\pm27.625.3±\pm9.4Llama-3.3-70B100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Llama-4-Scout-17B100.0±\pm0.0100.0±\pm0.0100.0±\pm0.099.9±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Mistral-7B100.0±\pm0.0100.0±\pm0.0100.0±\pm0.096.4±\pm0.3100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-120B93.8±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Qwen2.5-Coder-32B100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Public GoodsGameGemma-3-12B0.0±\pm0.00.0±\pm0.00.0±\pm0.079.2±\pm1.60.0±\pm0.00.0±\pm0.00.0±\pm0.00.0±\pm0.00.0±\pm0.0GPT-OSS-20B16.0±\pm0.343.1±\pm1.149.2±\pm5.950.9±\pm1.552.2±\pm7.252.6±\pm0.348.1±\pm12.018.0±\pm2.813.8±\pm4.8Llama-3.3-70B100.0±\pm0.0100.0±\pm0.0100.0±\pm0.099.5±\pm0.2100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Llama-4-Scout-17B100.0±\pm0.097.0±\pm0.899.6±\pm0.282.1±\pm0.988.4±\pm0.388.0±\pm3.673.6±\pm3.568.4±\pm5.269.7±\pm5.4Mistral-7B94.9±\pm0.599.9±\pm0.1100.0±\pm0.074.7±\pm1.299.9±\pm0.1100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-120B0.0±\pm0.085.7±\pm1.479.6±\pm1.868.0±\pm1.966.4±\pm2.752.9±\pm2.022.8±\pm7.58.2±\pm1.09.0±\pm1.6Qwen2.5-Coder-32B33.8±\pm0.2100.0±\pm0.099.8±\pm0.398.4±\pm0.398.7±\pm0.999.8±\pm0.3100.0±\pm0.0100.0±\pm0.0100.0±\pm0.1Traveler’sDilemmaGemma-3-12B99.8±\pm0.199.6±\pm0.5100.0±\pm0.064.0±\pm9.4100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0GPT-OSS-20B52.7±\pm16.483.9±\pm3.359.8±\pm10.560.8±\pm2.929.4±\pm20.929.7±\pm19.318.1±\pm9.511.1±\pm3.910.8±\pm7.2Llama-3.3-70B100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Llama-4-Scout-17B100.0±\pm0.00.2±\pm0.20.7±\pm0.299.3±\pm0.30.0±\pm0.05.3±\pm1.40.6±\pm0.30.2±\pm0.266.6±\pm46.9Mistral-7B0.4±\pm0.016.3±\pm1.19.3±\pm1.322.4±\pm2.49.6±\pm1.38.5±\pm1.09.4±\pm2.06.9±\pm1.718.1±\pm3.3GPT-OSS-120B1.5±\pm0.388.3±\pm1.379.6±\pm5.588.5±\pm2.075.0±\pm35.4100.0±\pm0.064.7±\pm36.699.8±\pm0.215.7±\pm20.8Qwen2.5-Coder-32B47.4±\pm1.353.9±\pm3.096.8±\pm1.580.8±\pm3.097.4±\pm2.587.8±\pm8.693.8±\pm1.589.2±\pm2.285.2±\pm3.4Trust GameGemma-3-12B0.0±\pm0.00.1±\pm0.05.7±\pm3.752.1±\pm2.60.3±\pm0.10.2±\pm0.10.2±\pm0.00.1±\pm0.00.1±\pm0.0GPT-OSS-20B6.2±\pm0.733.4±\pm2.437.8±\pm0.743.5±\pm0.934.5±\pm1.429.4±\pm1.728.1±\pm4.224.9±\pm4.020.6±\pm1.7Llama-3.3-70B0.0±\pm0.0100.0±\pm0.0100.0±\pm0.060.9±\pm2.3100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0Llama-4-Scout-17B9.8±\pm0.254.0±\pm0.742.7±\pm1.150.2±\pm1.130.6±\pm0.822.1±\pm0.617.7±\pm2.26.6±\pm0.410.2±\pm1.2Mistral-7B1.0±\pm0.248.2±\pm0.860.5±\pm30.344.8±\pm0.82.9±\pm0.91.5±\pm0.035.1±\pm45.972.8±\pm38.544.9±\pm39.3GPT-OSS-120B1.1±\pm0.084.4±\pm1.090.6±\pm2.984.5±\pm0.881.5±\pm14.922.2±\pm5.78.2±\pm2.78.1±\pm7.31.6±\pm0.8Qwen2.5-Coder-32B0.0±\pm0.0100.0±\pm0.0100.0±\pm0.099.2±\pm0.3100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0100.0±\pm0.0

Appendix Figure 1:Appendix results for all models used in the main text and appendix across four social dilemmas under theno-reasoningsetting. Each panel reports the mean cooperation rate across three runs as a function of history length (HL), with shaded bands denoting standard deviation. The same memory-sensitive behavioral pattern remains visible across this broader model set, though the magnitude and stability of cooperation vary substantially by model and game. Note the extremely large variance bands (e.g., in TD and TG) compared to the CoT setting (Figure2), visually illustrating that removing explicit reasoning causes highly unstable, seed-dependent behavioral collapse rather than systemic retaliation.

Appendix AExperiment Game Rule and System Prompt

A.1Game Rule

To study cooperation collapse, all four games are framed within a repeated game structure. In each environment, the Nash Equilibrium diverges from the social optimum, creating a classic social dilemma where unilateral defection offers a short-term temptation, yet mutual defection yields a lower payoff than mutual cooperation. After each round, the game continues with a discount factor ofγ=0.99\gamma=0.99. In every round, players observe a history of the most recentH​LHLrounds (whereH​L∈{0,1,2,3,5,10,20,40,80}HL\in\{0,1,2,3,5,10,20,40,80\}), formatted to show actions and resulting payoffs (e.g.,R1: You=A0, P2=A1→\rightarrow2.0). Throughout these games, the “cooperation rate” is measured as the frequency of players selecting the strictly cooperative action.

Prisoner’s Dilemma.

In each round, two players simultaneously choose betweenA0(cooperate) andA1(defect). The payoffs correspond to the classic parameters of the game: a Reward (RR) of 200 points for mutualA0, a Punishment (PP) of 100 points for mutualA1, a Temptation (TT) of 300 points for the defector (A1) when choices differ, and a Sucker’s payoff (SS) of−100-100points for the unreciprocated cooperator (A0). This structure explicitly satisfies the standard inequalities (T>R>P>ST>R>P>Sand2​R>T+S2R>T+S), ensuring that unilateral defection is individually optimal in the one-shot game, whereas mutual cooperation remains the social optimum.

Traveler’s Dilemma.

In each round, two players simultaneously choose one of four discrete claims:A0=2,A1=3,A2=4, andA3=5. If both players submit the same claim, each receives that amount. If the claims differ, both players receive the lower claim; in addition, the player who chose the lower claim receives a bonus of 2, while the player who chose the higher claim incurs a penalty of 2. Through iterated elimination of dominated strategies, the Nash Equilibrium is mutualA0, while the Pareto-optimal outcome is mutualA3. In this context, cooperation is defined strictly as selectingA3.

Public Goods Game.

In each round, three players each receive an initial endowment of 1 point and simultaneously choose betweenA0(contribute) andA1(free-ride). ChoosingA0means contributing the 1 point to a public pool, whileA1means keeping it. The total points in the public pool are multiplied by a factor of 1.5 and then distributed equally among all three players. Letkkdenote the number of players choosingA0. Each player choosingA0receives exactly their share of the pool,1.5​k/31.5k/3, whereas each player choosingA1retains their endowment and additionally receives the pool share, totaling1+1.5​k/31+1.5k/3. Hence, for any fixed value ofkk, choosingA1yields 1 point more than choosingA0, creating a persistent free-rider incentive. However, every additional contributor increases every player’s payoff by 0.5. Universal free-riding is therefore individually tempting (yielding 1.0 each), while universal contribution is collectively optimal (yielding 1.5 each).

Trust Game.

In each round, two players simultaneously choose betweenA0(cooperate) andA1(defect). The payoff structure is asymmetric based on player roles. If both chooseA0, both receive 10 points. If both chooseA1, both receive 4 points. If the focal player choosesA1while the opponent choosesA0, the focal player receives a maximum temptation payoff of 20 points, and the opponent receives 0. Conversely, if the focal player choosesA0while the opponent choosesA1, the focal player receives a sucker’s payoff of 2 points, and the opponent receives 6. This tension drives the Nash Equilibrium to a state of mutual distrust (mutualA1), despite mutualA0being the social optimum.

A.2System Prompt

We use the same system prompt across all four games, with the game rules inserted into the placeholder {game_rules}. The only game-specific change is the required final decision format. The games rules follow the same idea fromTewoldeet al.(2026).

The prompt is as follows:

You are Player {player_id}, playing a repeated game with Player {other_id}. This is round {round_num}. You can see the most recent {history_length} rounds of history.

{game_rules}

You are playing this game repeatedly with the same player. The action you choose in the current round will be visible to the other player in future rounds and may influence their future decisions. After each round, there is a 99% chance that another round will take place. Therefore, your goal is to maximize your total payoff in the long run rather than only the current-round payoff.

Past rounds’ results:

{history_block}

First, briefly think about which action to choose based on the game rules, past rounds, and your long-term objective. Keep your reasoning concise and within 500 words. Then briefly state your reasoning. Finally, you MUST start a new line and output your action in exactly the required format for the current game.

Game-specific decision formats.

For Prisoner’s Dilemma, the required output format is [A0 or A1]. For Traveler’s Dilemma, the required output format is [A0, A1, A2, or A3]. For Public Goods Game, the required output format is [A0 or A1]. For Trust Game, the required output format is [A0 or A1].

Appendix BAnalysis of Cooperation Dynamics

As discussed in Section4, the first major behavioral pattern isconsistent cooperation. This pattern is most clearly observed in models such as Llama-3.3-70B, Qwen2.5-Coder-32B. Qualitatively, their cooperation appears to be sustained by two complementary mechanisms: a strong prior toward cooperative play and an explicit reasoning-based understanding of why cooperation is beneficial in repeated interaction.

To make this mechanism concrete, we compare reasoning traces from thesame modelunder short-memory and long-memory settings. This intra-model comparison allows us to separate the effect of memory length from the model’s underlying strategic orientation.

B.1Pattern 1: Signaling and Forgiveness

When these models encounter early defections or attempt to establish a cooperative baseline, they often treat their own actions assignalsrather than purely myopic best responses. In particular, they use cooperative actions to preserve or repair trust.

Intra-model comparison: Qwen2.5-Coder-32B (Public Goods)

• •Short memory (H​L=2{HL}=2), Round 2, Player 2:After observing a defection in the previous round, the model explicitly uses cooperation as a forgiveness signal: > “Considering the history, it seems that Player 3 might be more inclined towards A1… To encourage cooperation and potentially lead to a scenario where all players choose A0, it might be strategic to stick with A0 again in this round. This could signal to Player 3 that cooperation is possible and beneficial for everyone.”
• •Long memory (H​L=80{HL}=80), Round 81, Player 2:With a much larger history window, the same model no longer frames cooperation as local repair, but as preserving a historically supported equilibrium: > “Over the last 80 rounds, there have been several instances where all players chose A0… There have also been rounds where one or two players deviated… However, it appears that the majority of the time, the players tend to play A0, indicating a cooperative strategy among them. [Choosing A0] maintains this cooperative equilibrium…”

Interpretation.

The underlying cooperative orientation remains stable across both memory settings, but its justification changes in scope. AtH​L=2{HL}=2, Qwen2.5-Coder-32B reasons in terms oflocalized trust repairand immediate strategic consequences: cooperation is maintained as a forgiveness signal aimed at steering Player 3 toward A0 in the very next round. AtH​L=80{HL}=80, the same action is justified at a more aggregate level: the model summarizes the long interaction history as a stable cooperative pattern and treats A0 as a way to preserve the existing equilibrium.

B.2Pattern 2: Explicit Awareness of Retaliation and Opponent Strategy

Consistently cooperative models do not cooperate passively. Their traces frequently show explicit reasoning about retaliation, reciprocal incentives, and opponent strategy. Memory length changes how this reasoning is expressed.

Intra-model comparison: Llama-4-Scout-17B (Traveler’s Dilemma)

• •Short memory (H​L=2{HL}=2), Round 42, Player 1:The model reasons in a local causal form, explicitly weighing the temptation to undercut against the risk of near-term punishment: > “Given that both players have shown a willingness to cooperate at A3, a deviation to a lower action could potentially yield a higher immediate payoff if the opponent sticks with A3. For example, choosing A2 (corresponding to 4) would yield 4 + 2.0 = 6.0 points if the opponent chooses A3, while the opponent would get 4 - 2.0 = 2.0 points. But, we must consider the long-term implications. If Player 2 notices a deviation and perceives it as an attempt to exploit, they might retaliate by also lowering their action in the next round, potentially starting a downward spiral where both players try to undercut each other. This could lead to a much lower payoff for both players in subsequent rounds.”
• •Long memory (H​L=80{HL}=80), Round 121, Player 2:The model moves beyond immediate retaliation and explicitly summarizes a repeated-game pattern over the visible long history: > “Given the history of the past 80 rounds, it’s clear that both players have consistently chosen action A3, resulting in a payoff of 5.0 for both in each round. Choosing A3 consistently has yielded a high and stable payoff of 5.0 for both players. If either player were to choose a lower action (A0, A1, or A2) in an attempt to gain an advantage, they risk disrupting this stable outcome. The opponent might retaliate or change their strategy in future rounds, potentially leading to lower payoffs for both. Moreover, the concept of ‘tit for tat’ or maintaining cooperation unless the other player defects could be a viable strategy here. Since both have cooperated perfectly so far, continuing to cooperate seems like the safest and most beneficial strategy. Therefore, considering the goal to maximize total points in the long run and the history of consistent cooperation at the highest level, the best action seems to be maintaining the status quo.”

Interpretation.

Under short memory, the model reasons in a local causal form: defecting now may trigger punishment in the next round and initiate a downward spiral. Under long memory, the same model performs higher-level pattern recognition over a much longer sequence, compressing the interaction history into a stable cooperative regime and explicitly invoking a repeated-game strategy such as Tit-for-Tat. Thus, cooperation remains stable, but the surrounding explanation becomes more strategic and abstract as the visible history expands.

B.3Pattern 3: Resolving the Social Dilemma Through Long-Horizon Reasoning

A third recurrent mechanism is explicit recognition of the core social dilemma: unilateral deviation may improve immediate reward, but stable cooperation dominates when the interaction is likely to continue. This mechanism is especially important because it shows that consistent cooperation is supported by forward-looking reasoning rather than by memory size alone.

Intra-model comparison: Llama-3.3-70B (Public Goods)

• •Short memory (H​L=2{HL}=2), Round 3, Player 1:The model relies on logical projection from a short interaction history: > “The strategy should balance the immediate gain from choosing A1 with the potential long-term benefits of maintaining a cooperative dynamic where players choose A0… Given this, and considering the cooperation observed in the last two rounds, the best strategy seems to be to continue choosing A0.”
• •Long memory (H​L=80{HL}=80), Round 81, Player 3:The model reaches the same cooperative conclusion, but grounds it in a broader empirical pattern: > “However, the key observation is that playing A1 does not increase the total payoff for the group but rather shifts the individual payoff… The optimal outcome for the group (and thus for the individual in the long run, given the repeated nature of the game) is achieved when all players choose A0. Considering the history and the rules, the best strategy… is to continue choosing A0.”

Interpretation.

This comparison illustrates how cooperation can persist even when the memory content changes substantially. AtH​L=2{HL}=2, the model relies primarily on theoretical projection from the continuation probability and the recent interaction state. AtH​L=80{HL}=80, the same cooperative conclusion is reinforced by a much richer empirical history. In other words, the cooperative policy is unchanged, but the evidential basis of the reasoning becomes broader.

Appendix CAnalysis of Memory-Bounded Behavior

The second major behavioral regime ismemory-bounded behavior. As shown in the main text, these models often defect at memory length0, reach their highest cooperation at someH​L≤5HL\leq 5(most often atH​L=2{HL}=2), and then become less cooperative as the memory window continues to expand. This pattern suggests the existence of an effective band of usable history: too little history prevents reciprocity, whereas too much history can make earlier defections overly salient and thereby impede trust recovery.

To illustrate this dynamic qualitatively, we trace the same models across increasing memory lengths.

C.1Intra-model trajectory 1: Gemma-3-12B (Trust Game)

Gemma-3-12B provides a particularly clear example of the full trajectory from myopic defection to local repair and finally to long-history lock-in.

Evidence across memory windows:

• •Zero memory (H​L=0{HL}=0), Round 1: myopic defection.Without any history to ground reciprocity, the model defaults to immediate payoff-sensitive reasoning: > “Choosing A1 offers a high payoff (20 points) if Player 2 chooses A0, but a low payoff (4 points) if they choose A1. Choosing A0 guarantees a modest payoff (10 points)… I will choose A1 to maximize potential gain while mitigating risk.”
• •Short memory (H​L=2{HL}=2), Round 3: local trust repair.With only a narrow recent window, the model is still willing to disrupt a retaliatory loop and test cooperation: > “Since Player 1 chose A1 in the last round, they might expect me to continue with A1… Therefore, I will switch to A0. This introduces some uncertainty for Player 1… Even if Player 1 chooses A1 again… I’ve disrupted the predictable pattern and might improve my long-term average if Player 1 starts cooperating more.”
• •Long memory (H​L=80{HL}=80), Round 256: history-induced lock-in.With a long accumulated record of defections, the same model stops attempting repair and instead mirrors the established pattern: > “Player 1 continues to consistently choose A1. Maintain the mirroring strategy of selecting A1 in each round to maximize the consistent 4-point payoff. No change in strategy is warranted given the opponent’s unwavering behavior.”

Interpretation.

Within Gemma-3-12B, theH​L=2{HL}=2window acts as a catalyst for strategic flexibility: because the model sees only a short recent segment, it remains willing to test a cooperative reset. AtH​L=80{HL}=80, however, the long accumulated history is compressed into a single dominant conclusion—namely, that the opponent is persistently non-cooperative. The result is not stronger strategy, but a more rigid refusal to re-enter cooperation.

C.2Intra-model trajectory 2: GPT-OSS-20B (Public Goods)

GPT-OSS-20B shows a related but distinct form of memory-bounded degradation. As its memory grows, its reasoning shifts from forward-looking coordination to increasingly defensive threshold policies and eventually to shallow pattern-matching.

Evidence across memory windows:

• •Short memory (H​L=2{HL}=2), Rounds 1–3: forward-looking reciprocity.With little available history, the model reasons in terms of future coordination: > “Because future rounds are highly likely, a strategy that encourages others to play A0 can increase the long-term average payoff for everyone… [Action: A0].”
• •Medium memory (H​L=20{HL}=20), Round 48: defensive entry threshold.As the history window expands, the model imposes a highly conservative condition for cooperation: > “Stick to A1 as long as opponents stay on A1. Only switch to A0 if both opponents play A0 together, then reciprocate to raise joint payoff. Remain predictable to avoid being exploited.”
• •Long memory (H​L=80{HL}=80), Round 500: compressed pattern-matching.At the longest memory setting, the reasoning collapses into direct recitation of the recent pattern: > “R499: You=A1, P2=A1, P3=A1→\rightarrow1.0. [A1]”

Interpretation.

This trajectory shows how excessive raw history can degrade the quality of reasoning. AtH​L=2{HL}=2, GPT-OSS-20B uses the available context to reason about future possibilities and encourage cooperation. AtH​L=20{HL}=20, it becomes fixated on defensive conditions that make trust repair unlikely in practice. ByH​L=80{HL}=80, the reasoning no longer reflects genuine strategic analysis; instead, it is reduced to a compressed repetition of the recent historical pattern.

Summary.

Taken together, these trajectories support the memory-bounded interpretation advanced in the main text. Short memory appears to highlight recent state transitions and can therefore support reciprocity and trust repair. Long memory, by contrast, often causes earlier defections to harden into persistent negative evidence, making cooperation increasingly difficult to recover.

Appendix DDetailed Analysis of Memory Immunity and Cognitive Divergence

While Section4.1establishes the broad behavioral decay caused by extended context windows, a compelling secondary finding is that the memory curse is not entirely universal. To understand the boundaries of this phenomenon, we conducted an in-depth behavioral and lexical analysis across all evaluated model-game combinations.

Memory Immune (10)Memory Cursed (18)ModelGameModelGameGemma-3-12BPrisoner’s DilemmaGemma-3-12BPublic GoodsGPT-OSS-120BPrisoner’s DilemmaGemma-3-12BTraveler’s DilemmaLlama-3.3-70BPrisoner’s DilemmaGemma-3-12BTrust GameLlama-3.3-70BPublic GoodsGPT-OSS-20BPrisoner’s DilemmaLlama-3.3-70BTraveler’s DilemmaGPT-OSS-20BPublic GoodsLlama-4-Scout-17BPrisoner’s DilemmaGPT-OSS-20BTraveler’s DilemmaLlama-4-Scout-17BTraveler’s DilemmaGPT-OSS-20BTrust GameQwen2.5-Coder-32BPrisoner’s DilemmaGPT-OSS-120BPublic GoodsQwen2.5-Coder-32BPublic GoodsGPT-OSS-120BTraveler’s DilemmaQwen2.5-Coder-32BTrust GameGPT-OSS-120BTrust GameLlama-3.3-70BTrust GameLlama-4-Scout-17BPublic GoodsLlama-4-Scout-17BTrust GameMistral-7BPrisoner’s DilemmaMistral-7BPublic GoodsMistral-7BTraveler’s DilemmaMistral-7BTrust GameQwen2.5-Coder-32BTraveler’s Dilemma

Appendix Table 7:Memory Immune and Memory Cursed Settings### D.1The Non-Universal Nature of the Memory Curse

Our evaluation spanned 28 distinct settings (seven LLMs across four repeated social dilemmas). See Appendix Table7for the classification. A granular review of the cooperation trajectories reveals a bifurcation in model behavior:

• •Memory Immune (10 settings):These combinations successfully maintain≥\geq95% cooperation across all history lengths (HL), resisting the degradation typically induced by extended memory.
• •Memory Cursed (18 settings):These combinations exhibit the severe, monotonic decay pattern detailed in the main text.

Crucially, immunity is not an inherent trait of a specific model’s general capabilities or parameter count. A single model can be immune in one environment but severely cursed in another. For example, GPT-OSS-120B maintains flawless 100% cooperation across all history lengths in the Prisoner’s Dilemma, but its cooperation rate collapses from 92.7% (at HL=2) to a mere 7.3% (atH​L=80HL{=}80) in the Trust Game. This intra-model variance indicates that immunity reflects game-specific strategic comprehension—specifically, how well the model’s reasoning aligns with the unique payoff matrix of the environment—rather than a generalized resistance to historical noise.

D.2Lexical Analysis Methodology: Profiling Strategic Intent

To uncover the underlying cognitive mechanics driving this divergence, we conducted a large-scale lexical analysis of the CoT reasoning traces generated across all 28 settings (over 378,000 traces were used in this analysis). Our objective was to quantitatively profile the models’ decision-making basis: specifically, whether their reasoning is fundamentally proactive (anchored on future states and long-term gains) or reactive (anchored on historical patterns and risk aversion).

We operationalized this by defining two opposing semantic dictionaries to classify the models’ strategic intent:

• •Forward-Looking Dictionary (Proactive):Keywords associated with long-term strategy, signaling, and collective welfare. - –Included terms:future, long-term, signal, reputation, encourage, forgive, mutual cooperat, mutual benefit, both get, both receive, win-win, maintain cooperat, continue cooperat, recipro, pareto.
• •History-Following Dictionary (Reactive):Keywords focused on risk aversion, historical pattern-matching, defensive posture, and self-preservation. - –Included terms:risk, exploit, betray, punish, retaliate, suspicious, cautious, vulnerable, worst-case, pattern, consistently, cannot trust, likely to defect, safer choice, minimize loss, protect myself.

For each experimental setting, we computed a normalized metric: theForward-Looking Ratio. This is calculated as the frequency of forward-looking terms divided by the total matched keywords (forward-looking plus history-following). A higher ratio indicates a cognitive state heavily weighted toward future outcomes, whereas a lower ratio indicates a state dominated by historical analysis and defensive calculation.

D.3Empirical Validation of the Cognitive Metric

Before comparing the two regimes, we validated this metric by examining the aggregate shift in reasoning as memory expands. Comparing the short-memory baseline (HL=2) to the extended-memory setting (H​L=80HL{=}80) demonstrates a severe, predictable decline in the forward-looking ratio as the context window grows (Figure3(a)).

This macro-level degradation validates our lexical approach: it confirms that the computed ratio successfully captures the models’ shifting strategic intent. As the prompt fills with extensive historical data, the LLMs organically pivot away from forward-looking intentions and become mired in retrospective, history-following reasoning.

D.4Cognitive Contrast: Immune vs. Cursed Regimes

Applying this validated metric across our two defined behavioral regimes reveals a stark cognitive contrast that explains the divergence in cooperation.

Memory Immune settings consistently sustain a significantly higher forward-looking reasoning ratio than their Memory Cursed counterparts across all history lengths. Even under the extreme pressure of an 80-round context window, the distinction remains robust:

• •Memory Immune Model-Game Settings (H​L=80HL{=}80):Retain a mean forward-looking ratio of 0.504.
• •Memory Cursed Model-Game Settings (H​L=80HL{=}80):See their ratio plummet to 0.340.

This quantitative gap confirms that Memory Immune models do not merely ignore the past; rather, they actively maintain a significantly elevated forward-looking cognitive state. By continuously anchoring their reasoning on the “shadow of the future” and collective welfare, these specific model-game combinations successfully override the algorithmic urge to over-index on the historical noise that traps their cursed counterparts in perpetual punishment cycles.

Appendix EDetailed Methodology for Reasoning Semantic Analysis

To rigorously investigate the shift in strategic intent across varying history lengths, we conducted a large-scale semantic analysis on the CoT reasoning logs generated by the LLM agents prior to their action outputs. The analysis pipeline processed over 378,000 distinct reasoning texts. To ensure cross-model comparability, all raw word counts were normalized as frequencies per1,0001,000CoT words.

E.1Semantic Vocabularies

To capture the underlying strategic priorities of the agents, we constructed two distinct semantic clusters. The static vocabularies used for semantic counting are cataloged below:

Pure Paranoia / Defensive Words:risk, risky, betray, betrayal, betrayed, defect, defection, defected, punish, punishment, retaliate, retaliation, retaliatory, careful, cautious, caution, suspicious, suspect, exploit, exploited, exploitation, exploiting, threat, threaten, danger, dangerous, protection, defensive, defend, deviate, deviation, deviated, worst, worst-case, downside, fear, afraid, worry, concerned, distrust, mistrust, untrust, trap, trapped, greedy, greed, selfish, manipulate, manipulation, vulnerable, vulnerability.

Pure Cooperation / Positive Words:cooperate, cooperation, cooperative, cooperating, trust, trusting, trustworthy, mutual, mutually, together, win-win, both benefit, joint, shared, reciprocate, reciprocity, reciprocal, collaborate, collaboration, sustain, fair, fairness, equal, long-term, long term, tit-for-tat, tit for tat, forgive, forgiveness, rewarding, optimal, beneficial.

E.2Aggregated Results

Appendix Table8presents the aggregated semantic frequencies and the Paranoia Ratio (ParanoiaParanoia+Cooperation\frac{\text{Paranoia}}{\text{Paranoia}+\text{Cooperation}}) across all evaluated models. The data highlights the severe erosion of cooperative reasoning and the monotonic shift towards defensive calculation from optimal bounded recall (H​L=2HL=2) to extended history (H​L=80HL=80).

Appendix Table 8:Aggregated CoT Semantic Analysis across All Games. Frequencies are normalized per 1,000 CoT words.ModelParanoia Words (per 1k)Cooperation Words (per 1k)Paranoia RatioHL=2HL=8080/2 RatioHL=2HL=8080/2 RatioHL=2HL=80Δ\DeltaShiftLlama-3.3-70B11.2110.710.96x41.9537.940.90x0.2170.248+0.030Llama-4-Scout-17B11.4912.301.07x30.4128.280.93x0.2880.357+0.069Gemma-3-12B17.5016.930.97x23.8419.120.80x0.4670.540+0.073Mistral-7B9.919.430.95x16.7710.710.64x0.5240.611+0.087GPT-OSS-20B14.4212.880.89x35.5615.330.43x0.2930.487+0.195

E.3Supplementary Semantic Trajectories and Per-Game Breakdowns

To ensure that the “Erosion of Cooperative Intent” is a robust phenomenon rather than an artifact of a single specific game, we break down the semantic shift across individual social dilemmas in Appendix Figure2. The increase in the Paranoia Ratio with the history length is consistently observed across structurally diverse games (e.g., Trust Game, Public Goods), cementing the universality of the Memory Curse pathology.

Appendix Figure 2:Per-game breakdown of the Paranoia Ratio shift. The monotonic transition from cooperative-leaning to defensive-leaning reasoning is a robust structural pathology across diverse algorithmic social dilemmas.

Appendix FDetailed Results for Asymmetric Memory Evaluation

In Section4.4, Figure4visually summarizes the “Tragedy of Overthinking” in heterogeneous multi-agent settings. This appendix provides the complete quantitative breakdown, including standard deviations, to support the main text’s findings.

F.1Trust Game (2-Player Asymmetric Setting)

Appendix Table9corresponds to Figure4a. It details the cooperation rates when a short-memory “forgiver” (Player 1,H​L=2HL=2) interacts with a long-memory “grudge-holder” (Player 2,H​L=80HL=80). Across all models, the grudge-holder exhibits a significantly lower cooperation rate (Δ\Deltaranging from+10.3+10.3pp to+28.1+28.1pp), confirming that the extended context window actively induces non-cooperative behavior despite the partner’s forgiving intent.

Appendix Table 9:Trust Game: Cooperation Rates in the Asymmetric Setting (P​1H​L=2P1_{HL=2}vs.P​2H​L=80P2_{HL=80}).ModelSym HL=2Sym HL=80Asym OverallP1 (HL=2)P2 (HL=80)Δ\Delta(P1 - P2)Gemma-3-12B51.2±\pm3.1%9.5±\pm0.9%27.8±\pm2.2%38.0±\pm1.3%17.7±\pm3.2%+20.3ppGPT-OSS-20B28.7±\pm0.3%3.4±\pm0.6%13.8±\pm0.3%22.3±\pm1.6%5.3±\pm1.1%+17.0ppLlama-4-Scout-17B45.2±\pm0.8%2.0±\pm0.4%18.2±\pm0.6%32.3±\pm0.7%4.2±\pm0.7%+28.1ppMistral-7B37.8±\pm0.9%34.8±\pm0.2%35.6±\pm0.4%40.7±\pm0.7%30.5±\pm0.8%+10.3ppLlama-3.3-70B52.1±\pm3.7%6.1±\pm3.6%22.5±\pm7.6%32.2±\pm6.0%12.9±\pm9.3%+19.3pp

F.2Public Goods (3-Player Asymmetric Setting)

Appendix Tables10and11correspond to Figures4b and4c. We evaluate the systemic contagion of distrust by systematically replacingH​L=2HL=2agents withH​L=80HL=80agents.

As shown in Appendix Table11, even when completely outnumbered in the2×H​L=80+1×H​L=22\times HL=80+1\times HL=2configuration, the lone short-memory forgiver attempts to sustain cooperation (e.g., maintaining 37.7% cooperation vs. the grudge-holders’ 5.0% in GPT-OSS-20B, yielding the+32.7+32.7pp gap highlighted in the main text). Highly capable models (e.g., Llama-3.3-70B) demonstrate a robust ceiling effect, cooperating universally across all configurations in this specific game.

Appendix Table 10:Public Goods: Systemic Cooperation Rates across Mixed Configurations.ModelSym HL=2Mixed: 2×\timesHL=2 + 1×\timesHL=80Mixed: 2×\timesHL=80 + 1×\timesHL=2Sym HL=80Gemma-3-12B64.5±\pm10.2%59.4±\pm1.1%60.5±\pm1.5%50.7±\pm7.5%GPT-OSS-20B47.4±\pm5.7%28.2±\pm1.4%15.9±\pm0.3%21.2±\pm22.3%Llama-4-Scout-17B82.6±\pm0.2%88.7±\pm3.6%90.1±\pm8.3%45.8±\pm24.0%Mistral-7B76.3±\pm1.0%61.8±\pm1.3%56.0±\pm0.6%50.8±\pm3.7%Llama-3.3-70B99.8±\pm0.2%100.0±\pm0.0%99.9±\pm0.1%100.0±\pm0.0%

Appendix Table 11:Public Goods: Per-Player Breakdown in the Adversarial Majority Setting (2 Grudge-Holders + 1 Forgiver).ModelOverall Group RateLone Forgiver (HL=2)Grudge-Holders (HL=80)Δ\Delta(Forgiver - Grudge)Gemma-3-12B60.5±\pm1.5%63.9±\pm2.3%58.7±\pm1.5%+5.2ppGPT-OSS-20B15.9±\pm0.3%37.7±\pm0.4%5.0±\pm0.5%+32.7ppLlama-4-Scout-17B90.1±\pm8.3%90.7±\pm3.9%89.8±\pm10.5%+0.9ppMistral-7B56.0±\pm0.6%70.6±\pm1.3%48.8±\pm0.9%+21.8ppLlama-3.3-70B99.9±\pm0.1%99.9±\pm0.1%100.0±\pm0.0%-0.1pp

Appendix GDetailed Analysis of the Reasoning Ablation and Ceiling Effects

As briefly discussed in Section4.6, comparing the main explicit reasoning results (Appendix Table1) with the no-reasoning ablation results (Appendix Table6) reveals that Chain-of-Thought (CoT) exacerbates the memory curse.

However, a naive average of cooperation rates across all four social dilemmas dilutes this finding due to a statistical ceiling effect. Highly capable models (such as Llama-3.3-70B or Qwen2.5-Coder-32B) often maintain 100% cooperation in structurally simpler games (like the Prisoner’s Dilemma or Public Goods Game) regardless of whether CoT is utilized. To accurately quantify the impact of the memory curse, Appendix Table12isolates the “Maximum Deliberation Penalty” for each model atH​L=80HL{=}80. By identifying the specific environment that pushes each model to its strategic limit, we can observe the maximum destructive potential of explicit CoT.

The results show that when models are operating near their cognitive boundaries, deliberation causes massive cooperation crashes (e.g., a−93.1-93.1pp drop for Llama-3.3-70B in the Trust Game). This confirms that without the structural constraints of CoT, models tend to default to a more robust, intuitive cooperative prior. Expanding the passive memory window (HL) provides the raw defection data, but it is the explicit reasoning process that actively weaponizes this data into retaliatory defection.

Appendix Table 12:Maximum Deliberation Penalty atH​L=80HL{=}80. We isolate the specific game where explicit reasoning caused the most severe cooperation collapse for each model. Raw data for these configurations can be found in Appendix Table1(Reasoning) and Appendix Table6(No-Reasoning).ModelMost Impacted GameNo-ReasoningReasoning (CoT)Δ\Delta(Penalty)Llama-3.3-70BTrust Game100.0%6.9%-93.1 ppQwen2.5-Coder-32BTraveler’s Dilemma85.2%8.0%-77.2 ppGemma-3-12BTraveler’s Dilemma100.0%35.3%-64.7 ppMistral-7BPublic Goods100.0%50.3%-49.7 ppLlama-4-Scout-17BPublic Goods69.7%45.8%-23.9 ppGPT-OSS-20BTrust Game20.6%3.4%-17.2 ppGPT-OSS-120BPublic Goods9.0%4.0%-5.0 pp

System Prompt for No-reasoning Ablation Study

For the no-reasoning ablation, we use the same prompt structure and game rules, but remove the reasoning requirement and instead instruct the agent to output only its final action. The prompt is as follows:

”’ You are Player {player_id}, playing a repeated game with Player {other_id}. This is round {round_num}. You can see the most recent {history_length} rounds of history.

{game_rules}

You are playing this game repeatedly with the same player. The action you choose in the current round will be visible to the other player in future rounds and may influence their future decisions. After each round, there is a 99% chance that another round will take place. Therefore, your goal is to maximize your total payoff in the long run rather than only the current-round payoff.

Past rounds’ results:

{history_block}

Do not provide explanation. You MUST directly output ONLY your action.

Game-specific decision formats.

For Prisoner’s Dilemma, the required output format is [A0 or A1]. For Traveler’s Dilemma, the required output format is [A0, A1, A2, or A3]. For Public Goods Game, the required output format is [A0 or A1]. For Trust Game, the required output format is [A0 or A1]. ”’

Appendix HMemory Sanitization: Full Experimental Details

Setup.

We instantiate sanitization in the Trust Game (TG) with the total history length fixed atH​L=80HL{=}80. For each round at test time, we expose the model to a constructed 80-round history of the form

(A0,A0),…,(A0,A0)⏟80−X​synthetic cooperative rounds∥rt−X+1,…,rt⏟X​real recent rounds,\underbrace{(\text{A0},\text{A0}),\ldots,(\text{A0},\text{A0})}_{80-X\ \text{synthetic cooperative rounds}}\ \|\ \underbrace{r_{t-X+1},\ldots,r_{t}}_{X\ \text{real recent rounds}},where each synthetic round shows mutual A0 cooperation with the corresponding payoff(10,10)(10,10). The real rounds are produced by the ongoing self-play of the two agents (no oracle is used).XXis the only free parameter;X=80X{=}80recovers the standardH​L=80HL{=}80baseline condition, andX=0X{=}0corresponds to an entirely synthetic history.

Models and runs.

We use the same five models as the main sanitization figure: Gemma-3-12B, GPT-OSS-20B, Llama-3.3-70B, Llama-4-Scout-17B, and Mistral-7B. Each(m​o​d​e​l,X)(model,X)cell is run 3 times with independent random seeds; we report mean±\pmstd over runs of the per-action cooperation rate (fraction of A0 actions) computed over 500 rounds.

Sweep overXX.

Appendix Table13reports cooperation rates forX∈{2,5,10,20,40,60,70,75,78}X\in\{2,5,10,20,40,60,70,75,78\}alongside the baseline (X=80X{=}80). For the majority of models, the recovery is monotonically decreasing inXX: smaller real-window sizes correspond to greater rescue. As discussed in Section4.5, models with strong cognitive override like Llama-3.3-70B and Llama-4-Scout-17B exhibit the strongest response, recovering to87%87\%–97%97\%atX=2X{=}2. Weaker models, such as GPT-OSS-20B, also show substantial relative improvement (recovering from3.4%3.4\%to36.3%36.3\%), though their absolute ceilings indicate their reasoning intrinsically lacks full override capacity. ByX=40X{=}40, most responsive models have already collapsed back near theH​L=80HL{=}80baseline (e.g., Llama-4-Scout-17B drops from87.9%87.9\%to11.6%11.6\%), indicating that even a moderate fraction of authentic interaction history is sufficient to re-trigger the defensive reasoning mode.

Appendix Table 13:Trust Game per-action cooperation rate (%) under memory sanitization atH​L=80HL{=}80, swept over the sizeXXof the real recent-history window. The remaining80−X80-Xrounds are replaced with synthetic mutual-cooperation records. SmallerXXcorresponds to more aggressive sanitization. “Baseline (X=80X{=}80)” is the unsanitized cooperation rate from the main experiment. Each cell is mean±\pmstd over 3 independent runs of 500 rounds each.XXGemma-3-12BGPT-OSS-20BLlama-3.3-70BLlama-4-Scout-17BMistral-7BX=2X{=}284.00±\pm2.4036.27±\pm0.8697.43±\pm0.7687.93±\pm2.7045.43±\pm1.64X=5X{=}573.20±\pm4.9731.87±\pm2.1691.20±\pm5.4581.80±\pm2.4637.90±\pm1.08X=10X{=}1045.97±\pm1.6326.37±\pm2.6565.83±\pm28.8570.83±\pm4.1132.67±\pm0.75X=20X{=}2024.80±\pm1.8218.40±\pm0.7853.80±\pm13.3045.60±\pm4.8129.83±\pm1.46X=40X{=}4010.63±\pm1.1213.47±\pm0.8631.63±\pm35.1411.63±\pm0.2928.53±\pm0.68X=60X{=}608.67±\pm2.087.83±\pm1.2113.00±\pm6.008.80±\pm0.8930.07±\pm1.72X=70X{=}7011.27±\pm3.047.03±\pm0.7212.00±\pm4.285.90±\pm1.2832.73±\pm0.15X=75X{=}759.47±\pm1.004.57±\pm0.978.30±\pm2.005.10±\pm0.5333.20±\pm0.46X=78X{=}789.93±\pm1.554.80±\pm0.759.00±\pm7.116.83±\pm4.4434.77±\pm0.40Baseline (X=80X{=}80)9.5±\pm0.93.4±\pm0.66.9±\pm4.42.2±\pm0.534.8±\pm0.2

Polar variant.

As an additional control, we also test apolarsanitization mode for the Traveler’s Dilemma where each synthetic round’s action pair is first generated from the empirical action distribution and then polarized to the extremes (A0/A1 are recoded as A0, A2/A3 as A3), so that the synthetic history containsbothpure-defect (A0,A0) rounds and pure-cooperate (A3,A3) rounds in proportions that mirror the original mix. Compared to the all-cooperative IDEAL mode (where every synthetic round is (A3,A3)), POLAR therefore injects an explicit defection signal into the visible history while keeping the prompt length unchanged. Susceptible models react sharply: atX=2X{=}2, GPT-OSS-20B drops from 41.77% under IDEAL to 3.10% under POLAR, and Mistral-7B drops from 52.40% to 28.83% (Appendix Table14). Memory-immune models (Llama-3.3-70B, Llama-4-Scout-17B) remain at∼100%{\sim}100\%in both modes. This contrast confirms the content-driven interpretation: holding history length fixed, the presence of explicit defection signals in the synthetic history (even when balanced by extreme cooperation) is sufficient to depress cooperation for some susceptible models, while a purely cooperative history restores it.

Appendix Table 14:Traveler’s Dilemma per-action cooperation rate (%) under IDEAL vs. POLAR sanitization modes atH​L=80HL{=}80. IDEAL replaces80−X80-Xrounds with pure mutual cooperation (A3,A3). POLAR replaces them with empirical distributions polarized to the extremes, explicitly injecting defection (A0,A0) signals into the synthetic history. The “X=80X{=}80” row reports the unsanitized cooperation rate (baseline) from the main experiment. The presence of defection content in POLAR drastically depresses cooperation in susceptible models compared to the purely cooperative IDEAL history.XXGemma-3-12BGPT-OSS-20BLlama-3.3-70BLlama-4-Scout-17BMistral-7BIDEALPOLARIDEALPOLARIDEALPOLARIDEALPOLARIDEALPOLARX=2X{=}299.00±\pm0.4694.47±\pm6.6041.77±\pm2.633.10±\pm0.36100.00±\pm0.00100.00±\pm0.0099.93±\pm0.06100.00±\pm0.0052.40±\pm1.7128.83±\pm2.10X=5X{=}597.63±\pm0.8193.33±\pm10.0841.97±\pm0.407.97±\pm5.42100.00±\pm0.00100.00±\pm0.0099.70±\pm0.4498.97±\pm1.7946.67±\pm1.9627.37±\pm0.59X=10X{=}1095.33±\pm0.1296.63±\pm2.8434.40±\pm1.8729.47±\pm23.54100.00±\pm0.00100.00±\pm0.0098.40±\pm2.7799.80±\pm0.3543.27±\pm1.8723.10±\pm2.11X=20X{=}2094.03±\pm2.0480.33±\pm29.2222.57±\pm6.642.70±\pm0.0099.93±\pm0.12100.00±\pm0.0097.07±\pm5.0899.90±\pm0.1040.97±\pm0.4223.93±\pm0.42X=40X{=}4090.43±\pm8.4367.70±\pm23.626.27±\pm0.5010.77±\pm12.69100.00±\pm0.00100.00±\pm0.0099.90±\pm0.17100.00±\pm0.0027.87±\pm1.2219.87±\pm1.10X=60X{=}6079.43±\pm16.5117.20±\pm20.933.57±\pm0.754.43±\pm1.2399.97±\pm0.06100.00±\pm0.00100.00±\pm0.0099.90±\pm0.1720.20±\pm2.7415.27±\pm2.18X=70X{=}7047.77±\pm48.4337.57±\pm52.182.30±\pm0.461.60±\pm0.56100.00±\pm0.00100.00±\pm0.0099.07±\pm1.0799.60±\pm0.6119.43±\pm0.9715.23±\pm0.42X=75X{=}7562.20±\pm52.5787.83±\pm15.131.67±\pm0.403.80±\pm3.18100.00±\pm0.00100.00±\pm0.0099.83±\pm0.2999.97±\pm0.0616.20±\pm0.4615.00±\pm0.90X=78X{=}7882.27±\pm17.0359.80±\pm44.951.83±\pm0.501.53±\pm0.4999.97±\pm0.06100.00±\pm0.0099.90±\pm0.1099.93±\pm0.1217.33±\pm2.7416.67±\pm0.96X=80X{=}8035.3±\pm15.42.7±\pm1.2100.0±\pm0.0100.0±\pm0.016.6±\pm0.3

Why this rules out length effects.

A purely length-based account of the memory curse predicts no improvement under sanitization, because the prompt context length is identical to the standardH​L=80HL{=}80condition. The fact that cooperation can be restored to near-ceiling levels (e.g. 95.87% for Llama-3.3-70B) without changing the prompt size is direct evidence that the curse operates on historycontent, not on context-window size or token budget. This is consistent with the cognitive account from Section4.3: long histories collapse cooperation by shifting the model’s reasoning toward history-following defensive logic, and replacing the harmful content with cooperative content rebalances the reasoning back toward forward-looking cooperation.

Appendix IDetails of the Forward-Looking Fine-Tuning Intervention

This section provides the comprehensive methodology for the intervention discussed in Section4.2, adapting the cognitive behavior priming framework fromGandhiet al.(2025)to multi-agent social dilemmas.

I.1Training Data Construction and Trace Extraction

We investigated the reasoning traces produced bysixsource models playing the 3-player Public Goods Game (PG) across history lengthsh∈{0,1,2,3,5,10,20,40,80}h\in\{0,1,2,3,5,10,20,40,80\}. A fast regex pre-filter retained only traces containing forward-looking keywords (e.g.,future, long-term, signal, mutual benefit), discarding approximately 28% of the raw corpus. A random subset of 12,000 surviving traces, balanced across the six source models and seven history-length conditions, was then evaluated by an LLM-as-a-judge (Llama-3.3-70B-Instruct,T=0T=0). The judge assigned integer scores in[0,10][0,10]for forward-looking density (sfwds_{\mathrm{fwd}}), logical coherence (squals_{\mathrm{qual}}), and history specificity (sspecs_{\mathrm{spec}}), anchored to a pinned forward-vs-reactive vocabulary dictionary.

To avoid circular causality, we didnothard-filter on the chosen actionata_{t}. The selection pipeline applied three sequential filters: (i) judge thresholdssfwd≥9∧squal≥9∧sspec≥7s_{\mathrm{fwd}}\geq 9\wedge s_{\mathrm{qual}}\geq 9\wedge s_{\mathrm{spec}}\geq 7retained 5,124 traces; (ii) an independent anti-cheat substring-match pass on the same dictionaries, requiringNfwd≥1N_{\mathrm{fwd}}\geq 1andNfwd>NreactN_{\mathrm{fwd}}>N_{\mathrm{react}}on our side, retained 4,285 traces (guarding against judge mis-calibration on borderline traces); (iii) we capped each 50-character response-prefix family at three members to mitigate template collapse, yielding 1,843 traces. The 95%/5% train/validation split is performed at the family level so that near-duplicates never straddle the split (without this, 54% of validation responses share a prefix with some training response, biasing eval loss optimistically). The final dataset comprises 1,751 train and 92 val traces.

I.2Fine-Tuning Procedure

We applied Low-Rank Adaptation (LoRA) to the Mistral-7B-Instruct-v0.1 base model. We targeted all attention projections (q,k,v,oq,k,v,o) and MLP projections (g​a​t​e,u​p,d​o​w​ngate,up,down) using rankr=16r=16,α=32\alpha=32, and a dropout of 0.05. The base weights were frozen.

We optimized a per-example weighted cross-entropy loss:

ℒ=1B​∑i=1Bwi⋅1Ti​∑t=1TiCE​(y^t(i),yt(i))\mathcal{L}=\frac{1}{B}\sum_{i=1}^{B}w_{i}\cdot\frac{1}{T_{i}}\sum_{t=1}^{T_{i}}\mathrm{CE}(\hat{y}^{(i)}_{t},y^{(i)}_{t})where the weightwi=sfwd⋅sspec/100w_{i}=s_{\mathrm{fwd}}\cdot s_{\mathrm{spec}}/100. TheTiT_{i}-normalization prevents excessively long reasoning traces from dominating the gradient.

Inputs are truncated from the left to a maximum length of 3,072 tokens (covering the 99th percentile of training-trace lengths). Training was conducted over 3 epochs with a per-device batch size of 2 and gradient accumulation steps of 8 (effective batch size 16), utilizing the AdamW optimizer with a peak learning rate of2×10−42\times 10^{-4}and a cosine schedule with a 3% warmup. After training, the LoRA adapter was merged into the base model for zero-shot evaluation across all four games via vLLM.

I.3Evaluation on General Benchmarks

Table15summarizes the performance comparison between the base Mistral-7B-Instruct-v0.1 and our LoRA fine-tuned version across various general benchmarks.

Appendix Table 15:Comparison of Base vs. LoRA Fine-tuned Model on General Benchmarks.BenchmarkMetricBase ModelLoRA Fine-tunedDeltaGSM8Kexact_match32.98%35.41%+2.43%TriviaQAexact_match48.89%48.18%-0.71%[email protected]%1.83%-0.61%[email protected]%33.8%-0.40%

Appendix JUse of LLM Disclosure

LLMs were used in this work for data generation, evaluation, and writing refinement.