Equilibrium Computation in Extensive-Form Games with Stochastic Action Sets

2026-06-11

AI Summary

Standard extensive-form games assume a fixed action set, which fails to capture real-world scenarios where exogenous stochasticity renders certain actions unavailable. This work proposes Extensive-Form Games with Stochastic Action Sets (EFGSAS), formally modeling this setting for the first time. Under an independence assumption, we prove the existence of a compact Nash equilibrium representation of polynomial size. Leveraging strategy expansion and compression techniques, we design the SI-CFR algorithm to minimize dormant internal regret, provably converging with high probability to a Nash equilibrium in two-player zero-sum EFGSAS. Furthermore, we employ stochastic approximation to recover a compact equilibrium from the sequence of iterates. This study provides the first practical solution framework for this class of games.

Abstract

Extensive-form games (EFGs) are a standard model for sequential decision-making in games. A fundamental and typically implicit assumption in EFGs is that players always have access to all of their actions at every decision point. However, in many realistic settings, certain actions might be unavailable during game-play due to exogenous stochasticity, hindering the expressivity of the standard EFG model. Given a `base' EFG, we formalize a model that allows for actions to be stochastically restricted, leading to a corresponding Extensive-Form Games with Stochastic Action Sets (EFGSAS). In EFGSAS, we derive an expansion procedure that results in an equivalent EFG, thus showing that standard strategy formalisms could require exponentially-large representations. However, under an appropriate independence assumption, we show that compact strategy representations polynomial in the size of the base EFG exist. Computationally, we introduce an algorithm called SI-CFR that minimizes sleeping internal regret, converging to Nash equilibria with high probability in two-player zero-sum EFGSAS. Finally, we utilize a stochastic approximation procedure to recover compact representations of Nash equilibria, utilizing only the iterates of SI-CFR.

Problem

• Extensive-form games
• Stochastic action sets
• Equilibrium computation
• Nash equilibrium
• Sequential decision-making

Innovation

• Extensive-Form Games with Stochastic Action Sets
• SI-CFR
• sleeping internal regret
• compact strategy representation
• Nash equilibrium