Extending Finite Memory Determinacy to Multiplayer Games

TL;DR

This paper extends finite memory determinacy results from two-player win/lose games to multi-player multi-outcome games, providing constructive proofs and algorithms for Nash equilibria.

Contribution

It generalizes previous results by establishing conditions under which finite memory strategies lead to Nash equilibria in complex multiplayer games.

Findings

Finite memory strategies suffice for Nash equilibria in certain multiplayer games.

Constructive proofs include upper bounds on memory requirements.

Algorithms for computing Nash equilibria are provided.

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. We provide a number of example that separate the various criteria we explore. Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant Nash equilibria.