Notice that here types, as opposed to players, maximize expected utility. This is because in type structure, beliefs are associated to types (see Section 2.3 above). The reader acquainted with decision theory will recognize that this is just the standard notion of maximization of expected utility, where the space of uncertainty of each player, i.e., the possible “states of the world” on which the consequences of her action depend, is the possible combinations of types and strategy choices of the other players.