Incentives and Implementation in Marriage Markets with Externalities

We study the implementability of stable correspondences in marriage markets with externalities. We prove that, contrary to what happens in markets 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.

We study assignment problems with externalities where agents have expectations about the reactions of other agents to group deviations. We present notions of core consistent with such expectations and identify the largest and smallest cores. 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 mechanisms.