Rationalizability in multicriteria games

We define rationalizability for multicriteria games and examine its properties. In a multicriteria game, each agent can have multiple decision criteria and thus has a vector-valued utility function. An agent’s rationalizable action is defined as such an action that can survive iterated elimination of never-Pareto optimal actions. We first generalize some properties of standard rationalizability such as existence to the multicriteria case. We then show that a rationalizable action in some weighted game is also rationalizable in the original multicriteria game, whereas the converse may not hold. This implies the robustness of non-rationalizable actions under utility aggregations for any weight vectors. We also discuss interpretations of mixed actions and their implications to multicriteria games.