Dual auctions for assigning winners and compensating losers

Abstract

We study the problem of allocating goods (or rights) and chores when participants have equal claim on a unit of the good or equal obligation to undertake a chore. We propose two dynamic auctions for solving problems of this type: a "goods" auction and a "chore" auction, which are duals of one another. Either auction can be used for allocating goods or chores by suitably defining a good or a chore. The auctions are efficient and payoff equivalent. We provide necessary and sufficient conditions for equilibrium for general utility functions for both auctions, and provide closed-form solutions when bidders are risk neutral and when they are CARA risk averse. The auctions have the same limit equilibrium bid function as bidders become infinitely risk averse. We show that the limit bid function is also the unique maxmin perfect strategy for both auctions.