Computing Evolutionarily Stable Strategies in Imperfect-Information Games

2025-12-10

AI Summary

This paper investigates the computability of evolutionarily stable strategies (ESS) in extensive-form games with imperfect information, symmetry, and perfect recall. We propose the first general-purpose algorithm enabling exact, complete (for non-degenerate cases), and anytime computation of ESS in such games—marking the first method to rigorously handle degenerate cases featuring infinitely many symmetric Nash equilibria. Our approach integrates extensive-form game tree traversal, symmetry-constrained modeling, linear complementarity problem (LCP) solving, equilibrium filtering, and iterative pruning. We validate the algorithm’s efficacy and scalability on cancer signaling games and randomly generated benchmarks: it enumerates all ESS in non-degenerate instances and efficiently computes representative ESS subsets in degenerate ones, supporting early termination.

Technology Category

Game Theory and Economic Paradigms: Imperfect InformationSearch and Optimization: Evolutionary ComputationMultiagent Systems: Mechanism Design

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsWeb Mining and Content Analysis: Models for Web evolution

Abstract

We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to multiplayer games. The algorithm is sound and computes all ESSs in nondegenerate games and a subset of them in degenerate games which contain an infinite continuum of symmetric Nash equilibria. The algorithm is anytime and can be stopped early to find one or more ESSs. We experiment on an imperfect-information cancer signaling game as well as random games to demonstrate scalability.

Problem

• Computes evolutionarily stable strategies in imperfect-information games
• Extends algorithm to multiplayer symmetric perfect-recall games
• Handles degenerate games with infinite Nash equilibrium continua

Innovation

• Algorithm for computing evolutionarily stable strategies
• Extends to multiplayer games from two-player base
• Anytime algorithm scalable in imperfect-information games