Abstract:

We study a variant of the house allocation problem (one-sided matching). Consider a continuum economy where N types of goods need to be allocated, one for each agent. All agents agree on the ranking of the basic goods and have quasi-convex preferences over lotteries. An optimal solution is a feasible allocation that is Pareto efficient and satisfies No Envy. We show that an optimal solution must give each agent a binary lottery, but identical agents may receive different lotteries. We prove the existence of an optimal solution when all individuals have the same preferences over lotteries, and provide sufficient conditions for existence if individuals' preferences are ranked in terms of risk aversion. If individuals satisfy the reduction of compound lotteries axiom, then the social planner can only deteriorate welfare by first randomizing over these binary lotteries, hence giving all agents the same lottery is never optimal. Full ex-ante equality can be achieved if agents satisfy the compound independence axiom.