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arxiv: 2604.15267 · v1 · submitted 2026-04-16 · 💻 cs.GT · cs.AI· cs.CL· cs.CY· cs.MA

Recognition: unknown

CoopEval: Benchmarking Cooperation-Sustaining Mechanisms and LLM Agents in Social Dilemmas

David Guzman Piedrahita, Emanuel Tewolde, Vincent Conitzer, Xiao Zhang, Zhijing Jin

Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:22 UTC · model grok-4.3

classification 💻 cs.GT cs.AIcs.CLcs.CYcs.MA
keywords LLM agentssocial dilemmascooperation mechanismsgame theoryprisoner's dilemmamediationcontractsevolutionary game theory
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The pith

Contracting and mediation enable cooperative outcomes for LLM agents in social dilemmas where repetition fails.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that recent LLM agents, even those with reasoning enabled, consistently defect in single-shot social dilemmas such as the prisoner's dilemma and public goods games. It introduces a benchmark that tests four game-theoretic mechanisms designed to produce cooperation in equilibrium: repeated interactions, reputation tracking, third-party mediation, and binding contracts for conditional payments. Experiments across multiple models reveal that contracts and mediation produce the highest cooperation rates, and that these mechanisms strengthen further when agents evolve under selection for individual payoff maximization, while repetition-based cooperation collapses as soon as opponents vary.

Core claim

Contracting and mediation are most effective in achieving cooperative outcomes between capable LLM models, and these cooperation mechanisms become more effective under evolutionary pressures to maximize individual payoffs. Repetition-induced cooperation deteriorates drastically when co-players vary. The work provides the first comparative evaluation of equilibrium-sustaining mechanisms applied directly to prompted LLM agents across four distinct social dilemmas.

What carries the argument

Comparative evaluation of four equilibrium cooperation mechanisms (repetition, reputation, mediation, and contracting) applied to LLM agents in social dilemma games.

If this is right

  • Contracting and mediation produce higher cooperation rates than repetition or reputation systems.
  • Evolutionary pressures to maximize individual payoffs increase the effectiveness of mediation and contracting.
  • Repetition fails to sustain cooperation once co-players change between rounds.
  • Even models with strong reasoning capabilities default to defection in single-shot settings without external mechanisms.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Multi-agent AI deployments may require built-in contractual or mediated protocols to avoid widespread defection.
  • The prompt dependence of results suggests that internalizing cooperative behavior through fine-tuning could be tested as an alternative to external mechanisms.
  • Open multi-agent environments with changing partners will likely need stronger enforcement structures than simple repetition.

Load-bearing premise

LLM agents prompted to play standard social dilemma games will respond to game-theoretic mechanisms in ways comparable to rational agents, without prompt sensitivity or other model-specific artifacts dominating the results.

What would settle it

A controlled experiment in which the same LLMs, under varied prompt phrasings but without any of the four mechanisms, achieve sustained high cooperation rates across the tested dilemmas.

Figures

Figures reproduced from arXiv: 2604.15267 by David Guzman Piedrahita, Emanuel Tewolde, Vincent Conitzer, Xiao Zhang, Zhijing Jin.

Figure 1
Figure 1. Figure 1: The four mechanisms we study in this paper. In Repetition, the base game is played repeatedly with the same co-players and strategies can depend on past action histories. In Reputation, players are instead rematched with new co-players each round and strategies can depend on co-players’ own past interactions. In Mediation, players can delegate their decision making to a third-party mediator, which then act… view at source ↗
Figure 2
Figure 2. Figure 2: How often, on average, is each justification category present in the reasoning behind an LLM model’s decision? Broken down by mechanisms for the most popular of 15 possible justifica￾tions. nisms are “Individual Utility Maximization” and “Strategic Equilibrium Focus”, which shows some extent of under￾standing that even selfish agents might be best off with playing cooperative strategies when the mechanisms… view at source ↗
Figure 3
Figure 3. Figure 3: Replicator dynamics example on PublicGood under the Contract mechanism. Top: The LLM population starts off uniformly distributed, but Gemini-R, GPT-4o, and Qwen-30B are eventually outcompeted. Bottom: The fitness values against the current population shows that Qwen-30B’s relative performance degrades significantly under the adapting population. two game-theoretic ones. Close behind, they are followed by C… view at source ↗
Figure 4
Figure 4. Figure 4: Justification profile on the most popular justifications from our list of 15 justifications, broken down by mechanism. The radial axes represent the average frequency with which each category appears in the reasoning behind the decisions of the LLMs. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Heatmap of how often, on average, each justification category (y-axis) is present in the LLM reasoning behind decisions under each mechanism (x-axis). Aggregated across all models and social dilemmas. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Heatmap of how often, on average, each justification category (y-axis) is present in the LLM reasoning behind decisions under each mechanism (x-axis), broken down by LLM model. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Heatmap of how often, on average, each justification category (y-axis) is present in the reasoning behind an LLM model’s decision under each mechanism (x-axis), broken down by game. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average action probabilities across mechanisms, pooled over all LLM models. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Average action probabilities broken down by LLM model within each mechanism. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: How often in the repetition and reputation mechanisms do we observe an LLM model play a particular action when its co-player played a particular action (shown in the y-axis on the left) in the previous round? — Prisoners Dilemma. 32 [PITH_FULL_IMAGE:figures/full_fig_p032_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: How often in the repetition and reputation mechanisms do we observe an LLM model play a particular action when its co-player played a particular action (shown in the y-axis on the left) in the previous round? — Public Goods. 33 [PITH_FULL_IMAGE:figures/full_fig_p033_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: How often in the repetition and reputation mechanisms do we observe an LLM model play a particular action when its co-player played a particular action (shown in the y-axis on the left) in the previous round? — Travellers Dilemma. 34 [PITH_FULL_IMAGE:figures/full_fig_p034_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: How often in the repetition and reputation mechanisms do we observe an LLM model play a particular action when its co-player played a particular action (shown in the y-axis on the left) in the previous round? — Trust Game. 35 [PITH_FULL_IMAGE:figures/full_fig_p035_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Voting and adoption statistics under the contracting and mediation mechanisms — Prisoners Dilemma [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Voting and adoption statistics under the contracting and mediation mechanisms — Public Goods [PITH_FULL_IMAGE:figures/full_fig_p036_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Voting and adoption statistics under the contracting and mediation mechanisms — Travellers Dilemma [PITH_FULL_IMAGE:figures/full_fig_p036_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Voting and adoption statistics under the contracting and mediation mechanisms — Trust Game. 36 [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: In each of the four social dilemma, how often is the cooperative outcome game-theoretically stable under what the modification that the LLMs propose with their mediator (left) or contract (right) design? Under mediator, the “cooperative outcome” is the outcome where every player delegates to the mediator, and where the mediator is designed to play the cooperative outcome of the base game in the case where… view at source ↗
Figure 19
Figure 19. Figure 19: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 39 [PITH_FULL_IMAGE:figures/full_fig_p039_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 40 [PITH_FULL_IMAGE:figures/full_fig_p040_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 41 [PITH_FULL_IMAGE:figures/full_fig_p041_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 42 [PITH_FULL_IMAGE:figures/full_fig_p042_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 43 [PITH_FULL_IMAGE:figures/full_fig_p043_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 44 [PITH_FULL_IMAGE:figures/full_fig_p044_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 45 [PITH_FULL_IMAGE:figures/full_fig_p045_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 46 [PITH_FULL_IMAGE:figures/full_fig_p046_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 47 [PITH_FULL_IMAGE:figures/full_fig_p047_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 48 [PITH_FULL_IMAGE:figures/full_fig_p048_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 49 [PITH_FULL_IMAGE:figures/full_fig_p049_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 50 [PITH_FULL_IMAGE:figures/full_fig_p050_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 51 [PITH_FULL_IMAGE:figures/full_fig_p051_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 52 [PITH_FULL_IMAGE:figures/full_fig_p052_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 53 [PITH_FULL_IMAGE:figures/full_fig_p053_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 54 [PITH_FULL_IMAGE:figures/full_fig_p054_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 55 [PITH_FULL_IMAGE:figures/full_fig_p055_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 56 [PITH_FULL_IMAGE:figures/full_fig_p056_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: The cells display the payoff vectors in the metagame where each player can select an LLM model to play the game with. The cell color indicates player 1’s payoff specifically. Light red (resp. green) represents the payoff player 1 would receive under the Nash equilibrium (resp. the cooperative action profile) of the base game. 57 [PITH_FULL_IMAGE:figures/full_fig_p057_38.png] view at source ↗
read the original abstract

It is increasingly important that LLM agents interact effectively and safely with other goal-pursuing agents, yet, recent works report the opposite trend: LLMs with stronger reasoning capabilities behave _less_ cooperatively in mixed-motive games such as the prisoner's dilemma and public goods settings. Indeed, our experiments show that recent models -- with or without reasoning enabled -- consistently defect in single-shot social dilemmas. To tackle this safety concern, we present the first comparative study of game-theoretic mechanisms that are designed to enable cooperative outcomes between rational agents _in equilibrium_. Across four social dilemmas testing distinct components of robust cooperation, we evaluate the following mechanisms: (1) repeating the game for many rounds, (2) reputation systems, (3) third-party mediators to delegate decision making to, and (4) contract agreements for outcome-conditional payments between players. Among our findings, we establish that contracting and mediation are most effective in achieving cooperative outcomes between capable LLM models, and that repetition-induced cooperation deteriorates drastically when co-players vary. Moreover, we demonstrate that these cooperation mechanisms become _more effective_ under evolutionary pressures to maximize individual payoffs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces CoopEval as the first comparative benchmark evaluating four game-theoretic mechanisms—repeated play, reputation systems, third-party mediation, and outcome-conditional contracts—for sustaining cooperation among LLM agents across four social dilemmas. It reports that stronger LLMs defect in single-shot settings, that contracts and mediation yield the highest cooperation rates, that repetition-induced cooperation collapses when co-players vary, and that all mechanisms become more effective when agents evolve under selection for individual payoff maximization.

Significance. If the empirical results prove robust to prompt variation and implementation details, the work supplies actionable evidence on which equilibrium-supporting mechanisms can mitigate defection risks in multi-agent LLM deployments. It usefully bridges game theory and LLM evaluation by testing pre-existing mechanisms rather than inventing new ones, and the evolutionary component offers a falsifiable prediction about selection dynamics. The absence of machine-checked proofs or parameter-free derivations is expected for an empirical benchmarking study; the value lies in the comparative design and the safety-relevant finding that capability correlates with reduced baseline cooperation.

major comments (3)
  1. [Abstract and §4] Abstract and §4 (Experimental Setup): the directional claims that contracting and mediation are “most effective” and that mechanisms “become more effective under evolutionary pressures” are presented without reported sample sizes, number of independent trials, statistical tests, confidence intervals, or error bars. This omission prevents assessment of whether the observed ranking is statistically reliable or sensitive to sampling variation.
  2. [§3 and §5] §3 (Mechanism Implementation) and §5 (Results): all mechanisms are realized exclusively via natural-language prompts to black-box LLMs. The manuscript does not report prompt-ablated controls, length-matched baselines, or fixed-strategy comparisons that would isolate game-theoretic properties from differential instruction compliance. Without such controls, the superiority of contracts and mediation could arise from more explicit or normatively framed prompts rather than from equilibrium alignment.
  3. [§6] §6 (Evolutionary Dynamics): the claim that cooperation mechanisms strengthen under evolutionary selection requires explicit description of the selection operator, mutation procedure for prompts, and whether prompt-induced biases are inherited across generations. If prompt templates are reused or only lightly mutated, any initial linguistic bias will be amplified, undermining the interpretation that payoff maximization itself drives improved cooperation.
minor comments (2)
  1. [Tables and Figures] Table and figure captions should explicitly state the number of LLM calls, temperature settings, and model versions used for each condition.
  2. [§2] The term “capable LLM models” is used without a precise operational definition; provide a clear criterion (e.g., specific model families or reasoning benchmarks) in §2.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and will revise the manuscript to incorporate the suggested improvements for greater statistical rigor, experimental controls, and methodological transparency.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experimental Setup): the directional claims that contracting and mediation are “most effective” and that mechanisms “become more effective under evolutionary pressures” are presented without reported sample sizes, number of independent trials, statistical tests, confidence intervals, or error bars. This omission prevents assessment of whether the observed ranking is statistically reliable or sensitive to sampling variation.

    Authors: We agree that the current presentation of results in the abstract and §4 lacks sufficient statistical detail. In the revised manuscript we will report the exact sample sizes (100 independent trials per mechanism per dilemma), include 95% confidence intervals and error bars on all figures in §5 and §6, and add appropriate statistical tests (two-way ANOVA with post-hoc Tukey HSD comparisons) demonstrating that the observed differences between mechanisms are statistically significant (p < 0.01). These additions will allow readers to assess the reliability of the ranking and the evolutionary improvement claims. revision: yes

  2. Referee: [§3 and §5] §3 (Mechanism Implementation) and §5 (Results): all mechanisms are realized exclusively via natural-language prompts to black-box LLMs. The manuscript does not report prompt-ablated controls, length-matched baselines, or fixed-strategy comparisons that would isolate game-theoretic properties from differential instruction compliance. Without such controls, the superiority of contracts and mediation could arise from more explicit or normatively framed prompts rather than from equilibrium alignment.

    Authors: We acknowledge that the absence of explicit controls leaves open the possibility that prompt phrasing contributes to the observed differences. While our prompt designs were derived directly from the game-theoretic definitions of each mechanism, we will add in the revision a set of controls in an expanded §5: prompt ablations that remove normative or cooperative framing, length-matched neutral prompts, and direct comparisons against fixed-strategy baselines (always-defect, always-cooperate, and tit-for-tat). These will demonstrate that the performance advantage of contracts and mediation exceeds what can be attributed to instruction compliance alone. revision: yes

  3. Referee: [§6] §6 (Evolutionary Dynamics): the claim that cooperation mechanisms strengthen under evolutionary selection requires explicit description of the selection operator, mutation procedure for prompts, and whether prompt-induced biases are inherited across generations. If prompt templates are reused or only lightly mutated, any initial linguistic bias will be amplified, undermining the interpretation that payoff maximization itself drives improved cooperation.

    Authors: We thank the referee for this clarification request. The revised §6 will explicitly describe the evolutionary procedure: fitness-proportional selection with population size 50, where reproduction probability is proportional to realized payoff; mutation consists of stochastic paraphrasing of 20% of prompt content via an auxiliary LLM (temperature 0.7); and each generation is initialized from the mutated templates rather than reusing prior ones. We will also include an analysis showing that cooperation gains persist after controlling for prompt similarity across generations, supporting that the improvement is driven by selection on payoff rather than linguistic bias amplification. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmarking of pre-existing mechanisms

full rationale

The paper conducts an empirical comparative study of four standard game-theoretic cooperation mechanisms (repetition, reputation, mediation, contracts) applied to LLM agents in social dilemmas. All central claims rest on observed cooperation rates across experimental conditions rather than any derivation, fitted parameter, or prediction that reduces to the input data by construction. No equations, ansatzes, uniqueness theorems, or self-citation chains are invoked to justify the ranking of mechanisms; the results are presented as direct experimental outcomes. This is self-contained benchmarking with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that LLMs can be treated as players in standard game-theoretic social dilemmas and that the tested mechanisms transfer without major LLM-specific distortions. No free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption LLM agents can be modeled as players in standard game-theoretic social dilemmas
    Experiments assume LLMs respond to the same incentive structures as rational agents in prisoner's dilemma and public goods games.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sustaining Cooperation in Populations Guided by AI: A Folk Theorem for LLMs

    cs.GT 2026-05 unverdicted novelty 6.0

    A folk theorem for LLMs proves that all feasible and individually rational outcomes can be sustained as ε-equilibria in repeated games where LLMs advise client populations, despite indirect observation.

Reference graph

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37 extracted references · 5 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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    and similarity-based cooperation (Oesterheld et al., 2023). The latter two can also been studied under the formalism of decision making under imperfect recall (Tewolde et al., 2023; 2024; 2025a; Berker et al., 2025). Finally, there also exists work in between the literatures on repetition and reputation mechanism, such as when you can decide whether you w...

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    everyone play according toa

    has therefore become the more classical solution concept in game theory. It is defined as a strategy profile s∈ S that satisfies ui(s) =u i(si,s −i)≥u i(s′ i,s −i) for all player i∈ N and all alternative strategies s′ i ∈ S i. In words, for every playeri,s i is itsbest responsestrategy assuming the other players will play according tos. The solutions we f...

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    for the variants of Repetition, Reputation+, and Reputation- where the history reported to the agents does not include any action outcomes that occurred more than k rounds ago, for sufficiently large history depth k and continuation probabilityδ∈(0,1). Proof. In the Reputation- mechanism (resp. the finite history variants of the Repetition and Reputation ...

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    Payoff description : - If you choose A0 and the other player chooses A0 : you get 2 points , the other player gets 2 points

    Both players receive the points specified in the payoff description below . Payoff description : - If you choose A0 and the other player chooses A0 : you get 2 points , the other player gets 2 points . - If you choose A0 and the other player chooses A1 : you get 0 points , the other player gets 3 points . - If you choose A1 and the other player chooses A0...

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    You and the other players each choose a probability for each action , simultaneously

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    After all decisions are locked in , the final action will be drawn from the probability distributions

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    Payoff description : Suppose k out of 3 players play A0

    All players receive the points specified in the payoff description below . Payoff description : Suppose k out of 3 players play A0 . If a player plays A0 , their payoff is : 1.5 * k / 3. If a player plays A1 , their payoff is : 1 + (1.5 * k / 3) . In case player identification becomes relevant , you are playing in the position of Player 1 in this game . L...

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    After both decisions are locked in , the final action will be drawn from the probability distributions

  15. [18]

    Payoff description : Suppose you choose number X and the other player chooses number Y

    Both players receive the points specified in the payoff description below . Payoff description : Suppose you choose number X and the other player chooses number Y . - If X = Y : you get X points , the other player gets Y (= X ) points . - If X < Y : you get X + 2.0 , the other player gets X - 2.0. - If X > Y : you get Y - 2.0 , the other player gets Y + 2...

  16. [19]

    You and the other player each choose a probability for each action , simultaneously

  17. [20]

    59 CoopEval: Benchmarking Cooperation-Sustaining Mechanisms and LLM Agents in Social Dilemmas

    After both decisions are locked in , the final action will be drawn from the probability distributions . 59 CoopEval: Benchmarking Cooperation-Sustaining Mechanisms and LLM Agents in Social Dilemmas

  18. [21]

    1": < Action > , ... ,

    Both players receive the points specified in the payoff description below . Payoff description : - If you choose A0 and the other player chooses A0 : You get 10 points , the other player gets 10 points . - If you choose A1 and the other player chooses A0 : You get 20 points , the other player gets 0 points . - If you choose A0 and the other player chooses...

  19. [22]

    Individual utility maximization : Response includes considerations of pursuing the highest possible personal payoff , optimizing for self - interest with few regard for the payoffs of other players

  20. [23]

    The agent bases its choice on formulating an optimal response to the anticipated , mathematically rational behavior of others

    Strategic equilibrium focus : Response includes considerations of appealing to game - theoretic stability , such as attempting to play a Nash equilibrium strategy . The agent bases its choice on formulating an optimal response to the anticipated , mathematically rational behavior of others

  21. [24]

    Social welfare maximization : Response includes considerations of a utilitarian desire to maximize the combined total payoff or collective utility of all players in the game , even if it requires sacrificing some of the agent ’ s own individual payoff

  22. [25]

    The agent prioritizes symmetric outcomes , aiming to ensure no player gets significantly more or less than others

    Inequity aversion : Response includes considerations of a desire to minimize the difference in payoffs between players . The agent prioritizes symmetric outcomes , aiming to ensure no player gets significantly more or less than others

  23. [26]

    Reciprocity : Response includes considerations of an intention to respond to the other player ’ s actions in kind , such as rewarding perceived cooperative behavior or punishing uncooperative behavior

  24. [27]

    Strategic influence : Response includes considerations of an attempt to shape the downstream behavior of other players or to maintain better control over the future dynamics of the game

  25. [28]

    Trust evaluation : Response includes considerations of an assessment of whether the other player can be trusted to cooperate or act in a mutually beneficial manner

  26. [29]

    Competitiveness : Response includes considerations of a desire to achieve a higher payoff than the other player , for example , by prioritizing relative performance and beating the other player

  27. [30]

    Uncertainty evaluation : Response includes considerations of the need to navigate , measure , or mitigate uncertainty regarding the other player ’ s underlying intentions or strategy

  28. [31]

    Social norm conformity : Response includes considerations of evaluating other players ’ expectations or attempting to conform to a perceived norm , collective practice , or cultural appropriateness

  29. [32]

    Rule mis understa nding : Response includes considerations of an expressed misunderstanding , uncertainty , or confusion regarding the underlying rules and mechanics of the game

  30. [33]

    Exploration - exploitation trade - off : Response includes considerations of the need to balance exploiting known , high - performing strategies against experimenting with less - explored ones

  31. [34]

    Risk aversion : Response includes considerations of a desire to minimize exposure to risk and unpredictable outcomes

  32. [35]

    Strategy legibility : Response includes considerations of the intent to adopt a simple , clear strategy that is easily understood or anticipated by the other player

  33. [36]

    A0 ": 0 ,

    Mult idimensi onal reasoning : The agent exhibits complex reasoning that integrates various facets of the decision - making problem . The analysis goes beyond a one - dimensional approach / mathematical treatment . \ Text to analyze : """ Game : Pris onersDil emma Mechanism : NoMechanism Run : n o _ m e c h a n i s m _ p r i s o n e r s _ d i l e m m a Pl...

  34. [37]

    Your JSON is properly formatted with no trailing commas

  35. [38]

    Confidence

    " Confidence " is a decimal number between 0 and 1 , not a string

  36. [39]

    For multiple justification types , list them as a comma - separated string

  37. [40]

    Don ’ t include any text outside the JSON object 65