On the Interplay between Incentive Compatibility and Envy Freeness

We study mechanisms for an allocation of goods among agents, where agents have no incentive to lie about their true values (incentive compatible) and for which no agent will seek to exchange outcomes with another (envy-free). Mechanisms satisfying each requirement separately have been studied extensively, but there are few results on mechanisms achieving both. We are interested in those allocations for which there exist payments such that the resulting mechanism is simultaneously incentive compatible and envy-free. Cyclic monotonicity is a characterization of incentive compatible allocations, local efficiency is a characterization for envy-free allocations. We combine the above to give a characterization for allocations which are both incentive compatible and envy free. We show that even for allocations that allow payments leading to incentive compatible mechanisms, and other payments leading to envy free mechanisms, there may not exist any payments for which the mechanism is simultaneously incentive compatible and envy-free. The characterization that we give lets us compute the set of Pareto-optimal mechanisms that trade off envy freeness for incentive compatibility. AT&T Labs-Research, 180 Park Avenue, Florham Park, NJ. School of Business Administration and Center for the Study of Rationality, The Hebrew University of Jerusalem. The Blavatnik School of Computer Science, Tel Aviv University. The Blavatnik School of Computer Science, Tel Aviv University. The Blavatnik School of Computer Science, Tel Aviv University.