Insights on the Theory of Robust Games

Document pages: 28 pages

Abstract: A robust game is a distribution-free model to handle ambiguity generated by abounded set of possible realizations of the values of players payofffunctions. The players are worst-case optimizers and a solution, calledrobust-optimization equilibrium, is guaranteed by standard regularityconditions. The paper investigates the sensitivity to the level of uncertaintyof this equilibrium. Specifically, we prove that it is an epsilon-Nashequilibrium of the nominal counterpart game, where the epsilon-approximationmeasures the extra profit that a player would obtain by reducing his level ofuncertainty. Moreover, given an epsilon-Nash equilibrium of a nominal game, weprove that it is always possible to introduce uncertainty such that theepsilon-Nash equilibrium is a robust-optimization equilibrium. An example showsthat a robust Cournot duopoly model can admit multiple and asymmetricrobust-optimization equilibria despite only a symmetric Nash equilibrium existsfor the nominal counterpart game.