Ideal equilibria in noncooperative multicriteria games

Abstract.

Pareto equilibria in multicriteria games can be computed as the Nash equilibria of scalarized games, obtained by assigning weights to the separate criteria of a player. To analysts, these weights are usually unknown. This paper therefore proposes ideal equilibria, strategy profiles that are robust against unilateral deviations of the players no matter what importance is assigned to the criteria. Existence of ideal equilibria is not guaranteed, but several desirable properties are provided. As opposed to the computation of other solution concepts in noncooperative multicriteria games, the computation of the set of ideal equilibria is relatively simple: an exact upper bound for the number of scalarizations is the maximum number of criteria of the players. The ideal equilibrium concept is axiomatized. Moreover, the final section provides a non-trivial class of multicriteria games in which ideal equilibria exist, by establishing a link to the literature on potential games.