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A note on k-price auctions with complete information when mixed strategies are allowed

Author

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  • Mathews, Timothy
  • Schwartz, Jesse A.
Abstract
Restricting attention to players who use pure strategies, Tauman (2002) proves that in a k-price auction (k≥3) for every Nash equilibrium in which no player uses a weakly dominated strategy: (i) the bidder with the highest value wins the auction and (ii) pays a price higher than the second-highest value among the players, thereby generating more revenue for the seller than would occur in a first- or second-price auction. We show that these results do not necessarily hold when mixed strategies are allowed. In particular, we construct an equilibrium for k≥4 in which the second-highest valued player wins the auction and makes an expected payment strictly less than her value. This equilibrium–which exists for any generic draw of player valuations–involves only one player using a nondegenerate mixed strategy, for which the amount of mixing can be made arbitrarily small.

Suggested Citation

  • Mathews, Timothy & Schwartz, Jesse A., 2017. "A note on k-price auctions with complete information when mixed strategies are allowed," Economics Letters, Elsevier, vol. 153(C), pages 6-8.
    • Handle: RePEc:eee:ecolet:v:153:y:2017:i:c:p:6-8
    DOI: 10.1016/j.econlet.2017.01.020
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    References listed on IDEAS

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    1. Tauman, Yair, 2002. "A note on k-price auctions with complete information," Games and Economic Behavior, Elsevier, vol. 41(1), pages 161-164, October.
    2. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    3. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    4. Azrieli Yaron & Levin Dan, 2012. "Dominance Solvability of Large k-Price Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-11, May.
    5. Dov Monderer & Moshe Tennenholtz, 2004. "K-price auctions: Revenue inequalities, utility equivalence, and competition in auction design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(2), pages 255-270, August.
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    Cited by:

    1. Nawar, Abdel-Hameed & Sen, Debapriya, 2018. "kth price auctions and Catalan numbers," Economics Letters, Elsevier, vol. 172(C), pages 69-73.

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    More about this item

    Keywords

    k-price auction;

    JEL classification:

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

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