Abstract:Large language models can score well on named game-theory benchmarks while failing on the same strategic computation once semantic cues are removed. We show this gap with procedurally generated zero-sum matrix games: a model that recognizes familiar games drops to 34%, 18%, and 2% success on anonymous $2{\times}2$, $3{\times}3$, and $5{\times}5$ payoff matrices. The benchmark separates semantic recall, learned approximate Nash computation, and an output-interface bottleneck that limits scale. Training only on $2{\times}2$ and $3{\times}3$ games, supervised fine-tuning raises unseen $5{\times}5$--$7{\times}7$ success from 2% to 61%, while exploitability-reward training averages 37% with high seed variance. We prove that the exploitability residual is $2$-Lipschitz in payoff perturbations, unlike discontinuous vertex-returning LP equilibrium selectors, explaining why residual training can transfer under payoff shifts even when formatting instability limits mean performance. A dominated-action padding experiment provides causal evidence: trained models solve $3{\times}3$ games embedded in much larger matrices, while random-padded controls fail and dense $12{\times}12$ games remain near failure. Procedural evaluation is therefore necessary for measuring strategic reasoning, and residual rewards expose a real but format-limited route to approximate equilibrium computation.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.10410 [cs.LG] |
| (or arXiv:2605.10410v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10410 arXiv-issued DOI via DataCite (pending registration) |
From: Wenhua Nie [view email]
[v1]
Mon, 11 May 2026 11:49:08 UTC (59 KB)
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