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Multi-bidder First Price Auction with Beliefs

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  • Hyeon Park

Abstract

This paper characterizes the set of equilibria in the first price auction with multiple bidders—specifically three bidders, each of whose type space is multi-dimensional, incorporating a bidder’s beliefs about others’ valuations. In this auction, each bidder independently and privately learns the other two opponents’ valuations with some probability. This paper derives closed form solutions for equilibrium bidding behaviours parameterized by the degree of information when the bidder has homogeneous beliefs regarding each opponent. This paper demonstrates how much the level of information affects the bidding behaviours of the informed bidders. In addition, this paper extends the model into N bidders when a high value bidder has fixed beliefs that all other bidders are identical types, and show how the value of information changes as the number of participants increases. Finally, this paper speculates on the possible changes in the efficiency of the model from increasing the valuation space to an arbitrary number. JEL Classification: D44, D82, D83

Suggested Citation

  • Hyeon Park, 2019. "Multi-bidder First Price Auction with Beliefs," Studies in Microeconomics, , vol. 7(1), pages 140-160, June.
    • Handle: RePEc:sae:miceco:v:7:y:2019:i:1:p:140-160
    DOI: 10.1177/2321022219850256
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    References listed on IDEAS

    as
    1. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    2. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    3. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    4. Hanming Fang & Stephen Morris, 2012. "Multidimensional Private Value Auctions," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 9, pages 319-356, World Scientific Publishing Co. Pte. Ltd..
    5. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    6. Helmuts Āzacis & Péter Vida, 2015. "Collusive communication schemes in a first-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 125-160, January.
    7. Kim, Jinwoo & Che, Yeon-Koo, 2004. "Asymmetric information about rivals' types in standard auctions," Games and Economic Behavior, Elsevier, vol. 46(2), pages 383-397, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    First price auction; information level; bidder’s beliefs; multidimensional type space;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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