Preference revelation games in school choice when students are naïve or strategic

Abdulkadiroglu, Che, and Yasuda (2011) consider the preference revelation games induced by the immediate acceptance and deferred acceptance mechanisms (henceforth, the IA and DA games, respectively) when students are naive or strategic. They study properties of a class of equilibria of the IA game in which some strategic student misrepresents his preferences with positive probability but they do not establish the existence of such equilibria. We show that in fact, depending on the parameters of the model, the IA game may have no such equilibrium. Then we provide a condition, termed richness, on the preference type space that ensures existence. Another result of Abdulkadiroglu, Che, and Yasuda (2011) is that in a symmetric equilibrium of the IA game, if a strategic student of some preference type reports his preferences truthfully, then a naive student of the same preference type is at least as well off in that equilibrium of the IA game as in the dominant strategy, truth-telling equilibrium of the DA game. This comparison, however, is silent on the welfare of the other naive students. We show that some naive students are indeed worse off under the immediate acceptance mechanism than under the deferred acceptance mechanism.