🤖 AI Summary
This work addresses the instability of traditional subgame solving in imperfect-information games, where reliance on Nash equilibrium often yields strategies with poor robustness in the full game. To overcome this limitation, the paper proposes using sequential equilibrium—a refinement of Nash equilibrium—as the solution concept for gadget games. By integrating sequence-form linear programming with an enhanced counterfactual regret minimization (CFR) algorithm, the method efficiently converges to this refined equilibrium with only minor additional computational overhead. Experimental results across multiple standard benchmark games demonstrate that the resulting strategies exhibit significantly improved consistency and reduced exploitability—by over 50% compared to unrefined Nash equilibrium strategies—thereby achieving markedly better global performance and robustness.
📝 Abstract
Subgame solving is a technique for scaling algorithms to large games by locally refining a precomputed blueprint strategy during gameplay. While straightforward in perfect-information games where search starts from the current state, subgame solving in imperfect-information games must account for hidden states and uncertainty about the opponent's past strategy. Gadget games were developed to ensure that the improved subgame strategy is robust against any possible opponent's strategy in a zero-sum game. Gadget games typically contain infinitely many Nash equilibria. We demonstrate that while these equilibria are equivalent in the gadget game, they yield vastly different performance in the full game, even when facing a rational opponent. We propose gadget game sequential equilibria as the preferred solution concept. We introduce modifications to the sequence-form linear program and counterfactual regret minimization that converge to these refined solutions with only mild additional computational cost. Additionally, we provide several new insights into the surprising superiority of the resolving gadget game over the max-margin gadget game. Our experiments compare different Nash equilibria of gadget games in several standard benchmark games, showing that our refined equilibria consistently outperform unrefined Nash equilibria, and can reduce the exploitability of the overall strategy by more than 50%