Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.10410 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911671555981312 |
|---|---|
| author | Nie, Wenhua Luo, Binhan Meng, Zijie Jang, Jyh-Shing Roger Ma, Ching-Wen |
| author_facet | Nie, Wenhua Luo, Binhan Meng, Zijie Jang, Jyh-Shing Roger Ma, Ching-Wen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10410 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equilibrium Residuals Expose Three Regimes of Matrix-Game Strategic Reasoning in Language Models Nie, Wenhua Luo, Binhan Meng, Zijie Jang, Jyh-Shing Roger Ma, Ching-Wen Machine Learning 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. |
| title | Equilibrium Residuals Expose Three Regimes of Matrix-Game Strategic Reasoning in Language Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.10410 |