Dual auctions for assigning winners and compensating losers

We study the bargaining problem of allocating homogeneous goods or chores when participants have equal claim to a unit of the good or equal obligation to undertake a chore. We propose two sequential auctions for solving problems of this type: a sequential ascending clock “goods” auction and a sequential descending clock “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 budget balanced, ex-post efficient and, when bidders are risk neutral, payoff equivalent. We characterize equilibrium bidding under constant absolute risk aversion and show that equilibrium converges to maxmin perfect bidding in the limit as bidders become infinitely risk averse. Connecting these results to cooperative game theory, we show that under maxmin perfect bidding the ascending clock goods auction gives each bidder his normative Shapley value allocation, while the descending clock chore auction gives each bidder his strategic Shapley value allocation. These two Shapley value allocations have different fairness interpretations, and thus the choice of the auction format determines which fair allocation results.