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Pure strategy equilibria of single and double auctions with interdependent values

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  • Araujo, Aloisio
  • de Castro, Luciano I.

Abstract

We prove the existence of monotonic pure strategy equilibrium for many kinds of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present an example of a double auction with interdependent values where all equilibria are trivial, that is, they have zero probability of trade. This is related to Akerlof's "market for lemmons" example and to the "winner's curse," establishing a connection between them. However, we are able to provide sufficient conditions for non-trivial equilibrium existence.

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  • Araujo, Aloisio & de Castro, Luciano I., 2009. "Pure strategy equilibria of single and double auctions with interdependent values," Games and Economic Behavior, Elsevier, vol. 65(1), pages 25-48, January.
    • Handle: RePEc:eee:gamebe:v:65:y:2009:i:1:p:25-48
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    Cited by:

    1. Luciano De Castro, 2012. "Correlation of Types in Bayesian Games," Discussion Papers 1556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. He, Wei & Sun, Xiang, 2014. "On the diffuseness of incomplete information game," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 131-137.
    3. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    4. Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. de Castro, Luciano I. & Riascos, Alvaro, 2009. "Characterization of bidding behavior in multi-unit auctions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 559-575, September.
    6. Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 407-440, June.
    7. Luciano I. De Castro & Alvaro Riascos, 2007. "Characterization of Bidding Behavior in Multi-Unit," Documentos CEDE 4382, Universidad de los Andes, Facultad de Economía, CEDE.
    8. Luciano Castro, 2011. "Equilibrium existence and approximation of regular discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 67-85, September.
    9. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    10. Pavlo Prokopovych & Nicholas C. Yannelis, 2022. "On nondegenerate equilibria of double auctions with several buyers and a price floor," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 625-654, April.
    11. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).

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