Computing Nash Equilibria in Multiplayer DAG-Structured Stochastic Games with Persistent Imperfect Information

TL;DR

This paper introduces an algorithm for approximating Nash equilibria in multiplayer stochastic games with persistent imperfect information, extending prior work to more complex, real-world scenarios.

Contribution

It presents a novel algorithm capable of handling multiplayer, general-sum stochastic games with persistent imperfect information, a significant extension over existing methods.

Findings

Algorithm effectively approximates Nash equilibrium in complex multiplayer scenarios.

Experimental results on a naval strategic planning game demonstrate the algorithm's practical utility.

Strategies computed are close to true Nash equilibria in tested scenarios.

Abstract

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has focused on two-player zero-sum games, games with perfect information, and games with imperfect-information that is local and does not extend between game states. We present an algorithm for approximating Nash equilibrium in multiplayer general-sum stochastic games with persistent imperfect information that extends throughout game play. We experiment on a 4-player imperfect-information naval strategic planning scenario. Using a new procedure, we are able to demonstrate that our algorithm computes a strategy that closely approximates Nash equilibrium in this game.