A Robust-optimization Approach to Uncertainty in Static Games

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JEL classification

• Optimization Techniques; Programming Models; Dynamic Analysis
• Noncooperative Games
• Firm Behavior: Theory

Keywords

Duopoly games, Robust Games, Robust-optimization equilibrium

Abstract

This paper focuses on the robust games proposed by Aghassi and Bertsimas (2006). They represent a distribution-free modelling framework for incomplete-information games, in which players are uncertain about the values of the parameters that define their own payoff functions. Each player is uncertainty averse in the sense that he/she max-imizes his/her worst-case payoff. Such a player is named a robust player, and a solution to this game is called a robust-optimization equilibrium. By focusing on non-cooperative, simultaneous-move, one-shot, finite games, we consider a general setting that includes both matrix and non-matrix games. Sufficient conditions for the existence of a robust-optimization equilibrium are provided. The result of existence proposed here is based on the Kakutani Fixed-Point Theorem. A few examples are provided that also include a robust duopoly game.