Auditing Game-Theoretic Measures of Strategic Reasoning in LLMs

Abstract

Game-theoretic benchmarks can separate distinct forms of strategic behavior in LLMs that aggregate theory of mind scores do not distinguish, but only if those benchmarks measure what they claim. We audit a four-game framework and a sealed-bid auction control based on 1,855 interactions among seven LLMs, correcting its first release against the raw transcripts. A 1,024-token completion limit caused some models to return empty answers that parsers silently replaced with fixed actions, invalidating the reported Kimi K2 profile and contaminating measurements in all game types. A solution of the implemented signaling game also replaces the previously reported equilibrium bluff target of 0.340 with a conditional rate of 2/3. On valid responses, bluff propensity ranges from 0.109 to 0.732 across models. A fitted model-specific propensity predicts held-out choices as well as or better than every equilibrium and QRE candidate tested. The equilibrium's type-level prescriptions are rejected for every model where they can be tested, and its aggregate rate keeps pace only when a model's own rate happens to be similar. Surviving valid cells cannot identify the previously reported cross-axis correlation. Finally, correcting an analysis-layer bug in the prompt-framing study reverses a prior result: reframing leaves Claude Haiku's bluff rate unchanged near 0.59 but raises GPT-4o-mini's greatly, from 0.08 to 0.65-0.67. Framing effects are model-dependent, and the measurements remain framing-conditional. We therefore treat fitted lambda values as payoff- and model-dependent summaries instead of structural rationality parameters. The transcript corpus and per-move validity masks are available at https://doi.org/10.5281/zenodo.21943627. The exact solver and correction pipeline will accompany a future release. Appendix itemizes the changes.