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Multiunit Pay-Your-Bid Auction with One-Dimensional Multiunit Demands

Author

Listed:
  • Bernard Lebrun
  • Marie-Christine Tremblay

Abstract

An arbitrary number of units of a good is sold to two bidders through a discriminatory auction. The bidders are homogeneous ex ante and their demand functions are two-step functions that depend on a single parameter. We characterize the symmetric Bayesian equilibrium and prove its existence and uniqueness. We compare this equilibrium with the equilibrium of the multiunit Vickrey auction and with the equilibria of the single-unit first price and second price auctions. We examine the consequences of bundling all units into one package. We study the impacts that variations of the "relative" supply have on the equilibrium, on the bidders' average payoffs per unit, and on the efficiency of the equilibrium allocation. Copyright 2003 By The Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

Suggested Citation

  • Bernard Lebrun & Marie-Christine Tremblay, 2003. "Multiunit Pay-Your-Bid Auction with One-Dimensional Multiunit Demands," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(3), pages 1135-1172, August.
    • Handle: RePEc:ier:iecrev:v:44:y:2003:i:3:p:1135-1172
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    Cited by:

    1. Jacob Goeree & Theo Offerman & Randolph Sloof, 2013. "Demand reduction and preemptive bidding in multi-unit license auctions," Experimental Economics, Springer;Economic Science Association, vol. 16(1), pages 52-87, March.
    2. Dirk Engelmann & Veronika Grimm, 2009. "Bidding Behaviour in Multi-Unit Auctions - An Experimental Investigation," Economic Journal, Royal Economic Society, vol. 119(537), pages 855-882, April.
    3. Ahmed Anwar, 2000. "Affiliation in Multi-Unit Discriminatory Auctions," Edinburgh School of Economics Discussion Paper Series 58, Edinburgh School of Economics, University of Edinburgh.
    4. Bresky, Michal, 2013. "Revenue and efficiency in multi-unit uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 82(C), pages 205-217.
    5. Takehito Masuda & Ryo Mikami & Toyotaka Sakai & Shigehiro Serizawa & Takuma Wakayama, 2022. "The net effect of advice on strategy-proof mechanisms: an experiment for the Vickrey auction," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 902-941, June.
    6. Takehito Masuda & Ryo Mikami & Toyotaka Sakai & Shigehiro Serizawa & Takuma Wakayama, 2020. "The net effect of advice on strategy-proof mechanisms: An experiment for the Vickrey auction," ISER Discussion Paper 1109, Institute of Social and Economic Research, Osaka University.
    7. Takehito Masuda & Ryo Mikami & Toyotaka Sakai & Shigehiro Serizawa & Takuma Wakayama, 2020. "The net effect of advice on strategy-proof mechanisms: An experiment for the Vickrey auction," ISER Discussion Paper 1109r, Institute of Social and Economic Research, Osaka University, revised May 2021.
    8. Takehito Masuda & Toyotaka Sakai & Shigehiro Serizawa & Takuma Wakayama, 2019. "A Strategy-Proof Mechanism Should Be Announced to Be Strategy-Proof: An Experiment for the Vickrey Auction," ISER Discussion Paper 1048, Institute of Social and Economic Research, Osaka University.
    9. Takehito Masuda & Toyotaka Sakai & Shigehiro Serizawa & Takuma Wakayama, 2019. "A Strategy-Proof Mechanism Should Be Announced to Be Strategy-Proof: An Experiment for the Vickrey Auction," ISER Discussion Paper 1048r, Institute of Social and Economic Research, Osaka University, revised Nov 2019.
    10. Wittwer, Milena, 2020. "Interconnected pay-as-bid auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 506-530.
    11. Burkett, Justin & Woodward, Kyle, 2020. "Uniform price auctions with a last accepted bid pricing rule," Journal of Economic Theory, Elsevier, vol. 185(C).

    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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