Allocating positions fairly: Auctions and Shapley value

We study the problem of fairly allocating heterogenous items, priorities, positions, or property rights to participants with equal claims from three perspectives: cooperative, decision theoretic, and noncooperative. We characterize the Shapley value of the cooperative game and then introduce a class of auctions for non-cooperatively allocating positions. We show that for any auction in this class, each bidder obtains his Shapley value when every bidder follows the auction’s unique maxmin perfect bidding strategy. When information is incomplete we characterize the Bayesian equilibrium of these auctions, and show that equilibrium play converges to maxmin perfect play as bidders become infinitely risk averse. The equilibrium allocations thus converges to the Shapley value allocation as bidders become risk averse. Together these results provide both decision theoretic and non-cooperative equilibrium foundations for the Shapley value in the position allocation problem. ∗The authors are grateful for comments from seminar participants at Cambridge University, Rice University, University of Texas Austin, Vanderbilt University, and participants at the 2017 NYUAD APET conference, the EWGET 2018 conference, and the 2018 CPMD Workshop on Market Design at University of Technology Sydney. The authors are also grateful for comments from Gabrielle Demange, David Pérez-Castrillo, Audrey Hu, and especially Herve Moulin. †Department of Economics, University of Tennessee (mvanesse@utk.edu). ‡Division of Social Science, New York University Abu Dhabi, and the Center for Behavioral Institutional Design. Wooders gratefully acknowledges financial support from the Australian Research Council’s Discovery Projects funding scheme (project number DP140103566) and from Tamkeen under the NYU Abu Dhabi Research Institute Award CG005.