Essays on Assignment Problems without transfers

Abstract

In Essays on Assignment Problems without transfers we study assignment problems with externalities where agents have expectations about the reactions of other agents to group deviations. We show some impossibility results about the existence of strategy-proof, individually rational and efficient mechanisms. Given these impossibility results, we proceed in two ways. First, we restrict the domain of preferences to study the relationship between essentially single valued cores and the existence of strategy-proof, individually rational, and efficient mechanism. Second, we restrict the model and change the concept of solution and we prove that, contrary to what happens in market without externalities, no stable revelation mechanism makes a dominant strategy for the agents on one side of the market to reveal their preferences. However, the stable correspondence is implementable in Nash equilibrium. Finally, inspired by the centralized admission system implemented by the National Autonomous University of Nicaragua in Managua, we prove that, in contexts where students have to submitted reduced profile of preferences, providing information about available seats during the admission process reduces unfairness in results.