Distributionally Robust Games with Risk-averse Players

TL;DR

This paper introduces a new class of distributionally robust games for risk-averse players, generalizing several classic game types and providing methods to compute equilibria under payoff uncertainty.

Contribution

The paper develops a novel distributionally robust game model that unifies and extends existing game frameworks, with a solution approach for equilibrium computation.

Findings

Equilibria can be derived from a multi-linear system of equations.

Special cases reduce to classical Nash games.

The model is applicable to real-world uncertain strategic scenarios.

Abstract

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that our "Distributionally Robust Game" constitutes a true generalization of three popular finite games. These are the Complete Information Games, Bayesian Games and Robust Games. Subsequently, we prove that the set of equilibria of an arbitrary distributionally robust game with specified ambiguity set can be computed as the component-wise projection of the solution set of a multi-linear system of equations and inequalities. For special cases of such games we show equivalence to complete information finite games (Nash Games) with the same number of players and same action spaces. Thus, when our game falls within these special cases one can simply solve the corresponding Nash Game. Finally, we demonstrate the applicability of our new model of games and highlight its importance.