Allocating positions fairly: Auctions and Shapley value

Matthew Van Essen and John Wooders

Journal of Economic Theory, 2021, vol. 196, issue C

Abstract: 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 non-cooperative. 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.

Keywords: Auction; Bayes Nash equilibrium; Maxmin; Shapley value; Heterogeneous units (search for similar items in EconPapers)
JEL-codes: D44 D63 D81 D82 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:196:y:2021:i:c:s0022053121001320

DOI: 10.1016/j.jet.2021.105315

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