On Rationalizable Outcomes in Private-Value First-Price Discrete Auctions

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On Rationalizable Outcomes in Private-Value First-Price Discrete Auctions

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Jack Robles
Makoto Shimoji

Abstract

In this paper, we extend the result of Dekel and Wollinsky ("Rationalizable Outcomes of Large Private-Value First-Price Discrete Auctions" Games and Economic Behavior, 2003) on rationalizable outcomes in first-price auctions. Dekel and Wollinsky show that under certain conditions, each player chooses a unique bid conditional on her valuation. Their result however depends on the assumption that the number of players is sufficiently large (relative to the number of available bids). We first provide a different set of sufficient conditions for the uniqueness result. We then show that for the independent (possibly asymmetric) private value case, (i) the result holds if the distributions are such that the inverse hazard rate is sufficiently high for each valuation, implying that auctions need not necessarily be large, and (ii) if the distributions satisfy the conditions of Dekel and Wollinsky, they always satisfy ours

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 09/21.

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Handle: RePEc:yor:yorken:09/21

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions

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Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October. [Downloadable!] (restricted)
Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Society for Economic Theory, vol. 2(1), pages 15-40, March. [Downloadable!]
Other versions:
- Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics. [Downloadable!]
Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 413-38, July.
Dekel, Eddie & Wolinsky, Asher, 2003. "Rationalizable outcomes of large private-value first-price discrete auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 175-188, May. [Downloadable!] (restricted)
Other versions:
- Eddie Dekel & Asher Wolinsky, 2001. "Rationalizable outcomes of large independent private-value first-price discrete auctions," Discussion Papers 1321, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]

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