An ASP-based approach to Solving General Stochastic Two-Player Games

2026-05-22

AI Summary

This work addresses the problem of solving two-player alternating games with stochasticity described in Game Description Language (GDL) by proposing a novel approach based on Answer Set Programming (ASP). It introduces Stochastic Quantified Answer Set Programming (SQASP), thereby extending ASP for the first time to stochastic GDL settings. The method formally models the maximum winning probability for a player and reduces the problem to an Extended Stochastic Satisfiability (XSSAT) formulation for solution. The paper contributes both a theoretical framework for SQASP and a corresponding translation-based solving mechanism. Experimental results on small stochastic games demonstrate that the approach achieves performance comparable to forward search, highlighting its potential for endgame evaluation in general game-playing systems.

Abstract

The Game Description Language (GDL) is a widely used formalism for specifying general games. Due to their similar syntax and semantics, Answer Set Programming (ASP) and its extensions have been applied to single- and two-player deterministic turn-taking GDL games. This paper presents the first ASP-based approach for solving two-player turn-taking GDL games with uncertainty. We introduce Stochastic An- swer Set Programming (SQASP) to encode the maximally achievable winning probability for a given player in stochastic GDL games, and develop a translation-based solver that evaluates SQASP programs by converting them to Extended Stochastic Satisfiability. Our empirical results show that the proposed approach is competitive with forward search on small stochastic games and can potentially support general game players in endgame evaluation.

Problem

• Stochastic Games
• Game Description Language
• Two-Player Games
• Uncertainty
• Winning Probability

Innovation

• Stochastic Answer Set Programming
• Game Description Language
• Two-player stochastic games
• Extended Stochastic Satisfiability
• General game playing