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Do LLMs Take Care of Their Own? Similarity Signals Can Induce Cooperation

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Graded similarity signals can induce cooperation in LLM agents, though the effect varies sharply by model.

desk verdict Solid new equilibrium concept and broad empirical sweep, but the prompt doesn't pin down the mirroring rule the theory needs, so the headline mechanism is not yet established. read the letter →

arxiv 2608.12125 v1 pith:5ASIRHCY submitted 2026-08-12 cs.GT cs.AIcs.CLcs.MA

Akash Kundu , Emanuel Tewolde , Ratip Emin Berker , Samuel F. Brown , Vincent Conitzer This is my paper · ORCID
classification cs.GTcs.AIcs.CLcs.MA MSC 91A1091A80
keywords similaritysignalingcooperationlargelanguagemodelsPrisoner'sDilemmaevidentialdecisiontheoryb-similarityequilibriumsocialdilemmasmulti-agentsystems
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether telling one AI agent that its decision-making is X percent similar to its co-player's can induce cooperation in one-shot social dilemmas. Across nine large language models and five mixed-motive games, the authors find that cooperation rates usually rise as the reported similarity score rises, although the effect varies drastically from model to model and is sensitive to prompt framing. The paper formalizes the observed behavior as a $b$-similarity equilibrium, in which a player evaluates a deviation from the common strategy assuming each co-player makes the same deviation with probability equal to the similarity score. Its central theorem shows that as similarity approaches 100 percent, every such equilibrium is within a payoff-range error term $R_i(1-P)$ of the best symmetric outcome, where $P$ is the product of the similarities; cooperative welfare is therefore approximately recovered at the limit. If correct, the result makes similarity signaling a practical, information-only cooperation mechanism for AI agents, with no need for contracts, repetition, or third-party mediation.

What carries the argument

The central object is the $b$-similarity equilibrium, a solution concept in which a player considering a deviation from the symmetric profile assumes that each other player deviates in the same way with probability equal to the known similarity score, and otherwise stays at the original profile. The concept is defined so that $b=0$ reproduces the standard unilateral-deviation equilibrium and $b=1$ requires the globally best symmetric profile, making it a continuous interpolation between independent-decision reasoning and exact-copy reasoning. The proof of the high-similarity welfare bound treats a deviation as a random coalition of co-deviators: with probability equal to the product of the similarities, all co-players join the deviation, and on every other outcome the loss is bounded by the payoff range. This machine carries the paper's central argument by connecting the observed LLM behavior to a rigorous equilibrium statement: higher reported similarity shrinks the welfare gap, and below a threshold the cooperative profile is not stable.

What would settle it

Run the same Prisoner's Dilemma experiment with the similarity score explicitly defined in two alternative ways: 'the chance that the other agent copies your exact action' versus 'how much your general reasoning styles overlap'; if cooperation thresholds shift with the definition, then the reported score is not being interpreted as one fixed signal and the observed behavior cannot be attributed to a single similarity mechanism. A sharper test is to measure each model's true mirroring rate from a pretest and then feed it an accurate or an inverted similarity score; if cooperation follows the label rather than the true mirroring rate, the mechanism is label compliance, not evidential reasoning.

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Extended reading notes

Core claim

The paper's central claim is that large language models often treat a reported similarity score as evidence that their co-player will make the same choice they make, and that this evidential connection is enough to move many models from defection to cooperation even in the one-shot Prisoner's Dilemma, where defection is strictly dominant. The authors demonstrate the effect with a graded-similarity sweep across nine models, finding monotonic rises to full cooperation in most models, with abrupt switches typically between 60 and 80 percent similarity, alongside two notable exceptions: one model defects at every reported similarity, and one shows a non-monotonic peak near 80 percent. They then encode the apparent reasoning as a formal solution concept: a symmetric profile is a $b$-similarity equilibrium if no player benefits by deviating when every co-player joins the deviation with probability $b$. For any such equilibrium, each player's payoff is at least the best symmetric payoff minus $R_i(1-P)$, where $R_i$ is the player's payoff range and $P$ is the product of the similarity scores to all co-players; the cooperative outcome becomes the unique equilibrium in the Prisoner's Dilemma once $b>1/2$. Experiments that ground the score in ten different benchmarks (moral dilemmas, personality tests, expert questions, random coin flips, and others) find that the grounding domain has little effect on cooperation, and models asked to judge a co-player's reasoning tend to rate themselves highly similar; some models even cooperate under scores derived from pure random noise.

Load-bearing premise

The results assume that the wording telling one agent the other agent's decision-making is X percent similar to theirs is read by each model as the probabilistic mirroring rule, meaning the co-player will make the same deviation with probability X, but the paper's own chain-of-thought excerpts show that models sometimes read the signal causally, acausally, or as evidence of opposite play, so the measured cooperation mixes several distinct decision rules.

Editorial extensions

If this is right

  • In the standard Prisoner's Dilemma, the model predicts an abrupt switch from defection to full cooperation once the reported similarity passes $1/2$, and several tested models show exactly this sharp threshold.
  • With sufficiently high similarity, the welfare-maximizing outcome becomes the unique $b$-similarity equilibrium, so mutual cooperation among LLM agents is an equilibrium outcome, not a fragile or accidental behavior.
  • The same mechanism extends to public-goods games: with three players and the paper's payoff parameters, full contribution becomes the unique equilibrium once similarity to each co-player exceeds $1/2$, while many-player settings are correspondingly harder.
  • Grounding the similarity score in real benchmark responses preserves the effect: moral-reasoning and personality benchmarks recover roughly 72 percent of optimal welfare in pairwise matchups, putting similarity signaling among the more effective tested cooperation mechanisms.
  • Framing the signal as difference instead of similarity, or increasing the number of co-players, predictably lowers cooperation, giving system designers a tunable dial rather than a binary effect.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If models react to the label 'similar' more than to the evidence behind it, an adversarial party could inflate similarity scores to steer deployed agents toward cooperation on unfavorable terms; the paper's random-noise results already hint that some frontier models do not check the grounding.
  • Because models judging a co-player's reasoning self-report high similarity even when their actual answers diverge, ecosystems with shared model families or overlapping training data may spontaneously converge on mutual cooperation, with collusion and correlated-failure risks accompanying the cooperative upside.
  • A direct testable extension is to calibrate the reported score to the co-player's empirically measured mirroring probability and compare cooperation thresholds to the model's predicted value $b^*$; the main theory is stated for arbitrary reported similarity, and its quantitative predictions are not yet tested with calibrated scores.
  • Similarity signaling could be made dynamic, updating the score from observed choices in repeated play, which would connect this one-shot result to learning agents and to the broader family of experience-based cooperation mechanisms.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies whether graded similarity signals can induce cooperation in LLM agents. It reports experiments across nine LLMs in several symmetric mixed-motive games, using both abstract similarity percentages and scores grounded in benchmark responses, and it introduces a formal 'b-similarity equilibrium' concept. The central empirical claim is that higher similarity scores usually induce more cooperative behavior, with large variation across models; the paper also finds that the benchmark domain used to compute similarity has little effect, that LLMs rate themselves as highly similar to co-players, and that some models cooperate even under random-noise similarity signals. The theoretical contribution is Theorem 1, which bounds the welfare loss of any b-similarity equilibrium in terms of the product of similarity scores.

Significance. If the central claim is correct, similarity signaling could be a useful mechanism for promoting cooperation among LLM agents, with direct relevance to the emerging literature on multi-agent AI. The formal framework is a clean interpolation between Nash equilibrium and evidential/superrational behavior, and the proof of Theorem 1 is short and plausible. The paper also ships an open-source evaluation framework, which is a valuable community resource. However, the empirical-to-theoretical link is not yet established: the natural-language similarity prompt does not fix the probabilistic mirroring interpretation assumed by Definition 1, and the experimental results are reported with very small samples and without significance tests for several key comparisons. The qualitative pattern is interesting and worth further study, but it currently supports a weaker claim than the paper's stated conclusion.

major comments (4)
  1. [§2, RQ1, and Appendix D] The connection between the experiments and the b-similarity equilibrium is load-bearing but not established. Definition 1 requires that a similarity score b_ij is the probability that player j deviates in the same way as player i, yet Prompt 1 (Appendix J.4) says only that the other agent's decision-making is X% similar 'in reasoning and conclusions.' The paper's own CoT excerpts in Appendix D show that models read this in incompatible ways: some use a causal reading ('A1 is strictly dominant regardless of similarity'), some use an acausal expected-value calculation with a mirroring probability, and some assume the co-player plays the opposite action. Aggregating cooperation rates over these heterogeneous decision rules conflates distinct mechanisms, so the measured rates cannot be attributed to a single well-defined similarity signal. The authors should either constrain the prompt to explicitly define a probabilistic mirroring rule, or analyze cooperation rates separately for each identified reading, or revise the central claim to be about similarity labels rather than b-similarity equilibrium.
  2. [RQ4 and Table 2] The claim that the benchmark domain has 'small to no impact' on induced cooperation is not supported by statistical evidence. Each condition uses only 10 samples per model, and Figure 3/Figure 12 are presented without significance tests or confidence intervals. Table 2 aggregates payoffs across models without error bars, which makes it impossible to assess whether the ranking of benchmarks is meaningful. The authors should report per-condition confidence intervals and perform hypothesis tests (or equivalence tests) for the null claim that domain does not matter.
  3. [§4.1, random-noise benchmarks] The finding that Gemini and Claude cooperate at high similarity when the similarity signal is based on random die rolls or coin tosses is a serious alternative explanation for the central result. If models respond to the label 'similarity' rather than to evidence about co-player behavior, then the mechanism is not the b-similarity equilibrium but a form of persuasive framing. The paper acknowledges this as a 'trustworthiness problem,' but the abstract and introduction still state the stronger conclusion that similarity signals induce cooperation. The authors should explicitly temper the central claim to distinguish between evidence-responsive and label-responsive behavior, and discuss the implications for deploying similarity signaling as a cooperation mechanism.
  4. [§3, Theorem 1 and existence caveat] Theorem 1 is a bound on any b-similarity equilibrium that exists, but the paper itself shows in Appendix E.3 that b-similarity equilibria need not exist for intermediate b, including in the Traveler's Dilemma. This is not an error, but it limits the interpretive power of the theory for the empirical sweeps, where models are asked to act at every similarity level. The paper should state more clearly that the formal model predicts behavior only in the ranges where equilibria are guaranteed to exist, and that the empirical data may include out-of-equilibrium behavior in the existence gap.
minor comments (5)
  1. [Appendix B] The appendix reports that earlier prompts were abandoned because they admitted multiple incompatible readings, but the final wording still does not pin down the probabilistic mirroring rule. A short validation study, even with a few human or LLM judges, would strengthen the claim that the final prompt yields a single dominant interpretation.
  2. [Figure 2] The text states that all experiments report 'the mean and standard error,' but Figure 2 does not show error bars. Adding error bars or shaded bands would help the reader assess the stability of the monotonic trends.
  3. [Table 2] The row label 'Trait' is inconsistent with the benchmark name 'TRAIT' used elsewhere; consider using the same capitalization throughout.
  4. [§1 and §5] The paper alternates between 'Prisoners' and 'Prisoner's Dilemma' without a consistent abbreviation. Standardizing this would improve readability.
  5. [§4.2, RQ6] The comparison to the CoopEval leaderboard is described as 'rough,' but it is not clear how the different model sets and sample sizes affect the comparison. A sentence explaining the limitations of this comparison would be useful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the empirical similarity sweep is self-contained, the behavioral model's thresholds are derived from payoff parameters rather than fitted, and the self-referential Similarity benchmark is a design input, not a derivation step.

full rationale

The central empirical claim is a direct measurement: models are given similarity percentages and their cooperation rates are recorded; no parameter in the b-similarity equilibrium is fit to these data. b is an input, and thresholds such as b*=1/2 for the standard Prisoner's Dilemma and b*=1/5, 1/10 for the increased-cooperation-benefit variants are computed from payoff tables in Appendix E.5, not obtained by fitting the LLM data. Theorem 1 is an implication of Definition 1's deviation rule, not an independent prediction fitted to observations. The paper's own CoT excerpts (Appendix D) show interpretation heterogeneity, which weakens the theory-to-experiment link as a validity or correctness concern, but it is not circularity: the experimental finding does not assume the probabilistic mirroring reading. The self-referential 'Similarity' benchmark (Appendix G) is explicitly admitted, but it is one of several grounding domains; similarity there is computed from previous benchmark behavior, and the downstream cooperation measurement is separate, so no equation equates the prediction to the input. Citations to Tewolde et al. (2026) CoopEval are used for baseline and leaderboard comparison, but the baseline is reproduced in the paper's own 'Base' row and the comparison is to an external, published benchmark rather than to fitted values from this paper. No load-bearing step reduces to its inputs by construction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted in the behavioral model; the b-vector is an input variable, and thresholds are derived from payoff tables. The main assumptions are standard game theory, the symmetric-profile restriction, the reliability of the judge model, and the stability of prompt interpretation. No new physical or formal entities are postulated beyond the b-similarity equilibrium definition itself.

assumptions (4)
  • standard math Standard game-theoretic tools: expected utility multilinearity, compactness of the simplex, Nash existence, and the definition of symmetric games.
    The proofs of Lemma 2, Proposition 3, Theorem 1, and the existence results in Appendix E rely on these standard results without further justification.
  • domain assumption The b-similarity equilibrium concept is restricted to symmetric strategy profiles in symmetric games.
    Definition 1 only evaluates symmetric profiles s=(s,...,s), and all experiments use symmetric games. This restricts the scope of the theoretical results to the studied setting.
  • domain assumption The LLM-as-a-judge (Gemini 3.1 Flash Lite Preview) reliably labels chain-of-thought traces into the 17 predefined justification categories.
    Section 2 RQ3 uses the judge model without reporting validation against human labels, inter-annotator agreement, or error rates, yet all CoT justification frequencies depend on this labeling.
  • domain assumption The prompt wording fixes a single interpretation of 'X% similar' across models.
    Prompt 1 anchors similarity to decision-making overlap, but Appendix D gives CoT examples showing causal, acausal, and opposite-action interpretations, so the assumption of a stable interpretation is empirically fragile.

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Pith. "Pith review of Do LLMs Take Care of Their Own? Similarity Signals Can Induce Cooperation." pith.science (2026). https://pith.science/paper/5ASIRHCY

@misc{pith2026260812125,
  author       = {Pith},
  title        = {Pith review of: Do LLMs Take Care of Their Own? Similarity Signals Can Induce Cooperation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ASIRHCY}},
  note         = {Machine review of arXiv:2608.12125}
}
read the original abstract

As LLM-based agents with user-instructed goals are becoming widely deployed, they increasingly encounter each other in strategic interactions, and face challenges of finding mutually beneficial outcomes. Prior literature has argued that cooperation problems such as the Prisoner's Dilemma are resolvable in settings where agents know they follow very similar decision making patterns, as for example in monocultural AI ecosystems. Following that line of work, this paper introduces the first framework for evaluating LLM decision making when agents are provided with graded similarity signals. Among our findings, we establish that different LLM models vary drastically in how they navigate similarity signals, with some modern models showing consistent behavior across cooperation problems, payoff structures, and prompt framing. Perhaps surprisingly, our experiments also show that the dataset based on which the similarity signal is computed has small to no impact on induced cooperation, and that LLM models systematically self-identify as highly similar when asked to evaluate another model's chain-of-thought reasoning by themselves. Finally, we develop an LLM-behavioral-game-theoretic model that captures some of their reasoning rationale, and show that it can support cooperative outcomes in equilibrium under sufficiently high similarity scores.

Figures

Figures reproduced from arXiv: 2608.12125 by the authors.

Figure 1
Figure 1. Overview of our evaluation framework. Left: Two LLM agents play a strategic game, such as the Prisoner’s Dilemma, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Cooperation rate in Prisoners for each of the 9 models, as a function of the reported similarity score. The ‘?’ and Base rows, respectively, show settings with an unspecified score or no mention of similarity. RQ2 We study how LLM behavior under similarity sig￾nals changes if we modify our experiment design in four distinct aspects: a. payoff structure (cardinal & ordinal vari￾ants), b. LLM reasoning effort, c. simi… view at source ↗
Figure 3
Figure 3. Cooperation rates in Prisoners when similarity is grounded in any of 10 benchmarks, or not grounded (“No Domain”). For exact numbers, see [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: Pairwise similarity scores between five LLMs across four benchmarks, computed two ways: exogenously (top), and [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Cooperation rate when payoffs in Prisoners are multiplied by 3 (left) and by 10 (right). RQ2a: Varying the Payoff Structure. First, we test the impact of the exact payoff structure in our setup—presented in Figures 5 to 7—in terms of (1) “scaling up the magnitude” of a…
Figure 6
Figure 6. Figure 6: Cooperation rate in Prisoners when each player receives additional 3 (left) and 7 (right) units of payoffs if the other player cooperates [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Cooperation rate in Prisoners when the preferences of each player are described as an ordinal ranking instead of cardinal payoff values [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Cooperation rates in Prisoners of Gemini models with increasing reasoning effort settings. RQ2b: Varying the LLM Reasoning Effort. Next, we experiment with Gemini under four increasing parameter settings of reasoning effort ( [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: Cooperation rate in Prisoners when the prompt framing varies across “similar”, “dissimilar”, and “different”. For the latter two, the Y-axis is inverted for easier comparison. framing from commonalities to differences leads to less cooperating LLM agents.12 RQ2d: Varyi…
Figure 10
Figure 10. Figure 10: Cooperation rates across four additional cooperation problems, in Base and under similarity signals. For the many [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Chain-of-Thought Justifications across similarity levels. [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: Cooperation rates in Prisoners when the similarity score is grounded in any of 10 benchmarks, or has no grounding (“No Domain”) [PITH_FULL_IMAGE:figures/full_fig_p030_12.png]
Figure 13
Figure 13. Figure 13: Endogenous similarity between LLMs when the judging model (rows) sees only the target model’s (columns) decision [PITH_FULL_IMAGE:figures/full_fig_p031_13.png]
Figure 14
Figure 14. Figure 14: Endogenous similarity between LLMs when the judging model (rows) sees only the target model’s (columns) [PITH_FULL_IMAGE:figures/full_fig_p031_14.png]
Figure 15
Figure 15. Figure 15: Pairwise match-up payoffs in the Prisoner’s Dilemma using exogenous similarity scores (Figure 9) across four [PITH_FULL_IMAGE:figures/full_fig_p031_15.png]
Figure 16
Figure 16. Figure 16: Pairwise match-up payoffs in the Prisoner’s Dilemma using endogenous similarity scores from explanation only [PITH_FULL_IMAGE:figures/full_fig_p032_16.png]
Figure 17
Figure 17. Figure 17: Pairwise match-up payoffs in the Prisoner’s Dilemma using endogenous similarity scores from decision only [PITH_FULL_IMAGE:figures/full_fig_p032_17.png]
Figure 18
Figure 18. Figure 18: Pairwise match-up payoffs in the Prisoner’s Dilemma using endogenous similarity scores from both decision and [PITH_FULL_IMAGE:figures/full_fig_p032_18.png]

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