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Bribing in First-Price Auctions: Corrigendum

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  • Kotowski, Maciej Henryk
  • Rachmilevitch, Shiran

Abstract

We clarify the sufficient condition for a trivial equilibrium to exist in the model of Rachmilevitch (2013). Rachmilevitch (2013), henceforth R13, studies the following game. Two ex ante identical players are about to participate in an independent-private-value first-price, sealed bid auction for one indivisible object. After the risk-neutral players learn their valuations but prior to the actual auction, player 1 can offer a take-it-or-leave-it (TIOLI) bribe to his opponent in exchange for the opponent dropping out of the contest. If the offer is accepted, player 1 is the only bidder and obtains the item for free; otherwise, both players compete non-cooperatively in the auction as usual. This is called the first-price TIOLI game.1 R13 shows that under the restriction to continuous and monotonic bribing strategies for player 1, any equilibrium of this game must be trivial—the equilibrium bribing function employed by player 1, if it is continuous and non-decreasing, must be identically zero. In this note, we clarify the sufficient conditions under which a trivial equilibrium exists. These are less stringent than originally proposed.

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  • Kotowski, Maciej Henryk & Rachmilevitch, Shiran, 2013. "Bribing in First-Price Auctions: Corrigendum," Scholarly Articles 10591649, Harvard Kennedy School of Government.
    • Handle: RePEc:hrv:hksfac:10591649
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    References listed on IDEAS

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    1. Eso, Peter & Schummer, James, 2004. "Bribing and signaling in second price auctions," Games and Economic Behavior, Elsevier, vol. 47(2), pages 299-324, May.
    2. Rachmilevitch, Shiran, 2013. "Bribing in first-price auctions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 214-228.
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    1. Hinloopen, Jeroen & Onderstal, Sander & Treuren, Leonard, 2020. "Cartel stability in experimental first-price sealed-bid and English auctions," International Journal of Industrial Organization, Elsevier, vol. 71(C).
    2. Aniol Llorente-Saguer & Ro’i Zultan, 2014. "Auction Mechanisms and Bidder Collusion: Bribes, Signals and Selection," Working Papers 734, Queen Mary University of London, School of Economics and Finance.
    3. Doğan, Serhat & Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2021. "Bribing in team contests," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 1-9.
    4. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    5. Troyan, Peter, 2017. "Collusion and signaling in auctions with interdependent values," Journal of Economic Theory, Elsevier, vol. 170(C), pages 319-345.
    6. Olga Gorelkina, 2014. "Bidder Collusion and the Auction with Target Bids," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2014_10, Max Planck Institute for Research on Collective Goods.
    7. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    8. Zheng, Charles Z., 2019. "Bidding collusion without passive updating," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 70-77.
    9. Aniol Llorente-Saguer & Ro’i Zultan, 2014. "Auction Mechanisms And Bidder Collusion: Bribes, Signals And Selection," Working Papers 1406, Ben-Gurion University of the Negev, Department of Economics.
    10. Llorente-Saguer, Aniol & Zultan, Ro’i, 2017. "Collusion and information revelation in auctions," European Economic Review, Elsevier, vol. 95(C), pages 84-102.
    11. Agranov, Marina & Yariv, Leeat, 2018. "Collusion through communication in auctions," Games and Economic Behavior, Elsevier, vol. 107(C), pages 93-108.

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