Games in Preference Form and Preference Rationalizability

We introduce a game in preference form, which consists of a game form and a preference structure, and define preference rationalizability that allows for each player's ex-post preferences over outcomes to depend on opponents' actions. We show that preference rationalizability is invariant to redundant types and states as long as all players have simplex restrictions on their ex-post preferences. We analyze the relationship between preference-form games and conventional payoff--form games. In particular, even if all players have simplex restrictions, we argue that there are multiple payoff-form games that correspond to a given preference-form game, and show that only one of them has the set of interim correlated rationalizable actions equal to the set of preference rationalizable actions in the preference-form game. We also discuss cases where the simplex assumption is violated.