Extending Finite Memory Determinacy to Multiplayer Games

TL;DR

This paper extends the concept of finite memory determinacy from two-player win/lose games to multi-player multi-outcome games on finite graphs, establishing conditions for Nash equilibria with finite memory strategies.

Contribution

It generalizes previous results by linking finite memory determinacy to Nash equilibria in multi-player games and provides constructive proofs with memory bounds and algorithms.

Findings

Finite memory determinacy implies Nash equilibria in multi-player games.

Counterexamples show the necessity of certain conditions.

Constructive proofs include algorithms for strategy computation.

Abstract

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player multi-outcome games. This generalizes a previous result by Brihaye, De Pril and Schewe. For most of our conditions we provide counterexamples showing that they cannot be dispensed with. Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant winning strategies.