Polynomial Expectation Property for Max-Polymatrix Games

TL;DR

This paper proves that a max-variant of polymatrix games has the polynomial expectation property, enabling the application of existing algorithms for correlated equilibria, and discusses potential extensions and broader implications.

Contribution

It establishes the polynomial expectation property for max-variant polymatrix games, opening avenues for computing correlated equilibria in these and related game variants.

Findings

Max-variant polymatrix games have the polynomial expectation property.

Results enable applying Papadimitriou and Roughgarden's methods.

Discussion on extending findings to other game variants.

Abstract

We address an open problem on the computability of correlated equilibria in a variant of polymatrix where each player's utility is the maximum of their edge payoffs. We demonstrate that this max-variant game has the polynomial expectation property, and the results of Papadimitriou and Roughgarden can thus be applied. We propose ideas for extending these findings to other variants of polymatrix games, as well as briefly address the broader question of necessity for the polynomial expectation property when computing correlated equilibria.