Do some AI models think harder about what their opponent is thinking when the game rewards bluffing and checking?

This explores which AI companies' models reasoned more deeply about what an opponent is thinking (mentalizing) in the inspection game than in rock-paper-scissors. The corpus retrieved for this question can't answer it. None of the twelve notes covers game-theoretic experiments, provider-by-provider comparisons, or opponent-modeling depth. I won't name providers or rankings, because anything I named would be invented.

The two games do test different things, which may be why a study would compare them. In rock-paper-scissors both players have symmetric options, and a player can do well just by tracking the opponent's recent moves, with no theory of the opponent's mind. In the inspection game, one side chooses whether to check and the other whether to cheat, and each side's best move depends on what it thinks the other believes. A model that mentalizes deeply would show it in the inspection game, where it must reason about the opponent's incentives, not just about patterns in past moves. That is general background, not something the corpus supports.

The closest material is a note on whether models can monitor their own thinking. It finds that Can language models genuinely monitor their own thinking? remains unresolved. The capability looks real but shallow and unevenly distributed, so it has to be tested task by task instead of trusted wholesale. That is about self-monitoring, not modeling an opponent. It suggests, but doesn't show, that a model's mentalizing depth could also vary sharply between games.

The rest of the retrieved set is about LLM judges and their biases, reasoning-length limits, and therapy-style conversation. None of it bears on this question. If you want this answered, the useful next step is a search on theory of mind, level-k reasoning, or strategic games in LLMs. The library may have a relevant paper under that vocabulary that this question's wording missed.