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Monotonicity and Rationalizability in a Large First Price Auction

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  • In-Koo Cho

Abstract

This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases ( Wilson, 1977 ). Instead of analysing the symmetric Nash equilibrium, we examine rationalizable strategies ( Bernheim (1984) , Pearce (1984) ) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighbourhood of the "truthful" valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to that of Wilson (1977) , while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighbourhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed. Copyright 2005, Wiley-Blackwell.

Suggested Citation

  • In-Koo Cho, 2005. "Monotonicity and Rationalizability in a Large First Price Auction," Review of Economic Studies, Oxford University Press, vol. 72(4), pages 1031-1055.
  • Handle: RePEc:oup:restud:v:72:y:2005:i:4:p:1031-1055
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    File URL: http://hdl.handle.net/10.1111/0034-6527.00360
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    Cited by:

    1. Azrieli, Yaron & Levin, Dan, 2011. "Dominance-solvable common-value large auctions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 301-309.
    2. Makoto Shimoji, 2017. "Revenue comparison of discrete private-value auctions via weak dominance," Review of Economic Design, Springer;Society for Economic Design, vol. 21(4), pages 231-252, December.
    3. 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.
    4. Mason, Robin & Valentinyi, Ã kos, 2007. "The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games," Discussion Paper Series In Economics And Econometrics 0710, Economics Division, School of Social Sciences, University of Southampton.

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