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Pure strategy equilibria of single and double auctions with interdependent values

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  • Castro, Luciano I. de
  • Araujo, Aloisio

Abstract

We prove the existence of monotonic pure strategy equilibrium for many types 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 a reasonable counterexample for interdependent values auctions that shows that sometimes all equilibria are trivial, that is, they have zero probability of trade. Nevertheless, we give sufficient conditions for non-trivial equilibrium existence.

Suggested Citation

  • Castro, Luciano I. de & Araujo, Aloisio, 2006. "Pure strategy equilibria of single and double auctions with interdependent values," UC3M Working papers. Economics we065320, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we065320
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    1. Fudenberg, Drew & Mobius, Markus & Szeidl, Adam, 2007. "Existence of equilibrium in large double auctions," Journal of Economic Theory, Elsevier, vol. 133(1), pages 550-567, March.
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    5. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-943, June.
    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 004382, UNIVERSIDAD DE LOS ANDES-CEDE.
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    14. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
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    18. Aloisio Araujo & Luciano I. de Castro Filho, 2004. "Pure Strategy Equilibria of Multidimensional and Non-Monotonic Auctions," Econometric Society 2004 Latin American Meetings 300, Econometric Society.
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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. Luciano I. De Castro & Alvaro Riascos, 2007. "Characterization of Bidding Behavior in Multi-Unit," DOCUMENTOS CEDE 004382, UNIVERSIDAD DE LOS ANDES-CEDE.
    3. He, Wei & Sun, Xiang, 2014. "On the diffuseness of incomplete information game," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 131-137.
    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. 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.
    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. 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.
    8. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.

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