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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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Keywords: First-Price Auctions; Rationalizability; Dominance;

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  1. repec:wop:humbsf:2000-72 is not listed on IDEAS
  2. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
  3. Eddie Dekel & Asher Wolinsky, 2001. "Rationalizable outcomes of large independent private-value first-price discrete auctions," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1321, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  5. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
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