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Allocating positions fairly: Auctions and Shapley value

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  • Van Essen, Matt
  • Wooders, John

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.

Suggested Citation

  • Van Essen, Matt & Wooders, John, 2021. "Allocating positions fairly: Auctions and Shapley value," Journal of Economic Theory, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:jetheo:v:196:y:2021:i:c:s0022053121001320
    DOI: 10.1016/j.jet.2021.105315
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    References listed on IDEAS

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    1. Matt Van Essen & John Wooders, 2023. "Dual auctions for assigning winners and compensating losers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1069-1114, November.

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    More about this item

    Keywords

    Auction; Bayes Nash equilibrium; Maxmin; Shapley value; Heterogeneous units;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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