Mechanism Design for Unequal Societies

Abstract

We study optimal mechanisms for a utilitarian designer who seeks to assign multiple units of an indivisible good to a group of agents with unit demand. The agents have heterogeneous marginal utilities of money, which implies that utility is not perfectly transferable between them. Heterogeneous marginal utilities of money may naturally arise in environments where agents have different wealth endowments. We show that the ex post efficient allocation rule is not optimal in our setting. Firstly, a high willingness to pay may stem from a low marginal utility of money. Moreover, the transfer rule does not only facilitate implementation of the desired social choice function in our setting, but also directly affects social welfare. In the optimal mechanism, rationing may occur, which entails a conflict between ex ante and ex post efficiency. In an extension, we show that it is still not utilitarian optimal to allocate the good solely based on willingness to pay even when redistribution is not possible. Finally, we highlight how our mechanism can be implemented as an auction with minimum bids and bidding subsidies.