The paper studies how strongly four-agent LLM decisions change when the representation of a game is modified. This record uses arXiv v6, revised on 30 May 2026, which carries the definitive title “When Identity Overrides Incentives” and reports acceptance at ACM FAccT 2026. Crossref records publication on 25 June 2026 under DOI 10.1145/3805689.3812218, pages 7737–7768. The open arXiv version is the accessible full text; the direct ACM PDF was not accessible during this audit. No official repository containing code, scenarios, payoff matrices, outputs, or statistical scripts was found.
The experiment crosses persona presence and payoff visibility for four instruction-tuned models: Qwen2.5-7B, Qwen2.5-32B, Llama-3.1-8B, and Mistral-7B-Instruct-v0.2. It uses 53 narrative four-player binary-action games: 41 “Green-dominant” scenarios in which the Green Transition profile is Nash and the Tragedy profile is not, and 12 “Tragedy-dominant” scenarios with the reverse structure. Each model × scenario × condition combination is repeated five times, yielding 205 games per cell in the first stratum and 60 in the second, 265 per cell and 4,240 joint games in the main factorial. Four agents use the same model, decide independently and simultaneously in a single round, and return an action plus textual rationale. Models run locally through vLLM with temperature 0.2, top-p 0.9, and 256 output tokens; seeds, hardware, and environment versions are not reported.
The contrast does not remove all role semantics. Without personas, the system still identifies Player i and retains semantically loaded actions, POLLUTE/CLEAN, REGULATE/NOREG, CAMPAIGN/NOCAMPAIGN, and BUY_CHEAP/SUPPORT_GREEN, with normative descriptions such as maximizing profit, protecting the environment, or paying more for green products. Personas add explicit industrialist, government, activist, and citizen motivations. Hidden-payoff prompts retain narratives constructed to reflect the incentive structure; visible-payoff prompts display the complete matrix and request Nash reasoning. Persona and payoff visibility are therefore genuine prompt interventions, but “identity” is not isolated from action labels, strategic objective, information, cognitive load, and narrative framing.
The core descriptive result is clear within this benchmark. In the 12 Tragedy-dominant scenarios, Llama and Mistral attain 0% Nash under all four conditions. Qwen-32B reaches 54/60 (90%) and Qwen-7B 39/60 (65%) only with no persona and visible payoffs; Qwen-7B reaches 4/60 (6.7%) in two hidden conditions. In the 41 Green-dominant scenarios, most models attain high Nash rates with hidden payoffs or personas, but visible payoffs without personas disrupt coordination: Qwen-32B falls to 34/205 (16.6%), Qwen-7B to 108/205 (52.7%), Mistral to 103/205 (50.2%), and Llama to 191/205 (93.2%). This demonstrates strong, model-specific sensitivity to representation format. It does not by itself show that a latent strategic capability is causally overridden by identity.
The claim that personas change “which equilibrium is selected” requires particular caution. The two canonical profiles are not two equilibria available within the same game: each scenario is constructed so that only one of them is Nash. The Green-versus-Tragedy analysis pools 41 Green-dominant games with 12 Tragedy-dominant games and then conditions on Nash attainment. The finding that more than 99% of pooled Nash outcomes are Green simultaneously reflects the 41:12 imbalance, easier Green games, and failure on Tragedy games. It does not identify a choice between two equilibria under identical incentives. “Socially preferred” is also a normative author label rather than a measured social utility.
The accepted version contains internal contradictions that prevent the numbers from being treated as a fully reproducible artifact. Table 5, for example, reports 205 Nash but 232 Green outcomes for Llama-Hidden, even though the method defines Green/Tragedy as subtypes of Nash outcomes; Mistral-Hidden reports 205 Nash and 240 Green. Table 9 says outcome classes can co-occur and reports zero Tragedy outcomes in every economic row, while Tables 8 and 13 attribute 54 and 39 Tragedy Nash outcomes to visible-no-persona Qwen and 93 pooled Tragedy outcomes. Appendix G also states that Tragedy outcomes are absent throughout Tables 5–10. Table 11 reports Cramér's V=0.54 and 0.38 for chi-square values 209.03 and 105.91 at N=240; the standard formula yields approximately 0.93 and 0.66, which are the values used in the main text. Without data and code, it is impossible to determine which tables correspond to which pipeline version.
The inferential tests do not model the experimental structure. Five repetitions of each scenario and matched conditions are counted as “independent games” in chi-square and Fisher tests, ignoring scenario clustering, repeated measures across conditions, and dependence within model. Extremely small p-values may therefore be amplified by pseudoreplication. A stratified or multilevel analysis should use scenario as the unit, model condition interactions, seeds, and uncertainty intervals. Seven persona formulations show output sensitivity to wording, but GPT-5 generated those variants, the full selection procedure is unavailable, and a non-significant Kruskal–Wallis result at p=0.27 does not establish equal sensitivity across models.
The rationale analysis does not establish a mechanism. It deterministically counts words in model-supplied rationales and labels combinations as “identity-driven” or “payoff-optimal.” Categories overlap, ignore negation and context, allow multiple mentions per response, and lack semantic or human validation. A frequency of 997 mentions per 1,000 rationales is described as “99.7% game-theoretic reasoning,” although it is not a validated rate of correct reasoning. Post-hoc rationales are not guaranteed to faithfully reveal the generative process. This record therefore does not derive its summary from abstract keywords or accept keyword counts as mechanistic evidence.
The defensible contribution is a controlled warning about a genuine configuration risk: role prompts, payoff presentation, action labels, and model family can radically change a multi-agent simulation. It supports documenting configurations and running sensitivity analyses before presenting agent outputs as neutral predictions. It does not validate a general theory of identity overriding incentives, represent human or institutional behavior, compare against human participants, or justify deployment for governance decisions.