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Dual Auctions for Assigning Winners and Compensating Losers

Author

Listed:
  • John Wooders
  • Matt Van Essen

    (Division of Social Science)

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 deÖning 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.

Suggested Citation

  • John Wooders & Matt Van Essen, 2018. "Dual Auctions for Assigning Winners and Compensating Losers," Working Papers 20180013, New York University Abu Dhabi, Department of Social Science, revised Jan 2018.
    • Handle: RePEc:nad:wpaper:20180013
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    References listed on IDEAS

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    Cited by:

    1. Yan Long, 2020. "Optimal budget-balanced ranking mechanisms to assign identical objects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 467-502, September.
    2. Van Essen, Matt & Wooders, John, 2021. "Allocating positions fairly: Auctions and Shapley value," Journal of Economic Theory, Elsevier, vol. 196(C).
    3. Matt Van Essen & John Wooders, 2025. "Mimic martingales in sequential auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(4), pages 1283-1310, June.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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