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On Rationalizability and Beliefs in Discrete Private-Value First-Price Auctions

Author

Listed:
  • Robles Jack

    (Victoria University of Wellington, jack.robles@vuw.ac.nz)

  • Shimoji Makoto

    (University of York, makoto.shimoji@york.ac.uk)

Abstract

We extend Dekel and Wolinsky's (2003) result on private-value first price auctions by providing different sufficient conditions under which each player has a unique rationalizable bid conditional on her value. Unlike Dekel and Wolinsky's, our result does not necessarily require a large number of players. If values are independently distributed, (i) our conditions are weaker than Dekel and Wolinsky's, and (ii) our conditions require a large number of players only if the distributions on values has a low reverse hazard rate for some value. Our result holds for the cases where players' utility functions are concave or values are not identically distributed.

Suggested Citation

  • Robles Jack & Shimoji Makoto, 2012. "On Rationalizability and Beliefs in Discrete Private-Value First-Price Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-21, May.
    • Handle: RePEc:bpj:bejtec:v:12:y:2012:i:1:n:16
    DOI: 10.1515/1935-1704.1829
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    References listed on IDEAS

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    1. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 413-438.
    2. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    3. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    4. In-Koo Cho, 2005. "Monotonicity and Rationalizability in a Large First Price Auction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 1031-1055.
    5. Robert Wilson, 1977. "A Bidding Model of Perfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 511-518.
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    Cited by:

    1. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
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    3. Bernhard Kasberger & Karl H. Schlag, 2024. "Robust Bidding in First-Price Auctions: How to Bid Without Knowing What Others Are Doing," Management Science, INFORMS, vol. 70(7), pages 4219-4235, July.
    4. 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.

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