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Simultaneous Bidding in Sealed-bid Auctions

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  • Silvio Sorbera

Abstract

In this paper, we analyze a model of competing sealed-bid first-price and second-price auctions where bidders have unit demand and can bid on multiple auctions simultaneously. We show that there is no symmetric pure equilibrium with strategies that are increasing in the lowest type, unlike in standard auction games. However, for a two-player game a symmetric mixed-strategy equilibrium exists, and bidders place bids on all available auctions with probability one. This holds true for any mixed equilibrium and for any number of bidders. We then solve the case of two auctions and two bidders. Analyzing the case of binary type space, we are able to identify mixed strategy equilibria and analyze the consequences of discrete bid spaces.

Suggested Citation

  • Silvio Sorbera, 2025. "Simultaneous Bidding in Sealed-bid Auctions," CRC TR 224 Discussion Paper Series crctr224_2025_713, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2025_713
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    References listed on IDEAS

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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