Rationalizable strategies in games with incomplete preferences

Abstract

This paper introduces a new solution concept for games with incomplete preferences. The concept is based on rationalizability and it is more general than the existing ones based on Nash equilibrium. In rationalizable strategies, we assume that the players choose nondominated strategies given their beliefs of what strategies the other players may choose. Our solution concept can also be used, e.g., in ordinal games where the standard notion of rationalizability cannot be applied. We show that the sets of rationalizable strategies are the maximal mutually nondominated sets. We also show that no new rationalizable strategies appear when the preferences are refined, i.e., when the information gets more precise. Moreover, noncooperative multicriteria games are suitable applications of incomplete preferences. We apply our framework to such games, where the outcomes are evaluated according to several criteria and the payoffs are vector valued. We use the sets of feasible weights to represent the relative importance of the criteria. We demonstrate the applicability of the new solution concept with an ordinal game and a bicriteria Cournot game.