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Isotone Equilibrium in Games of Incomplete Information

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David McAdams

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Abstract

An isotone pure strategy equilibrium exists in any game of incomplete information in which each player's action set is a finite sublattice of multidimensional Euclidean space, types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "nonprimitive conditions" whenever others adopt isotone pure strategies: (i) single-crossing in own action and type and (ii) quasi-supermodularity in own action. Conditions (i), (ii) are satisfied in supermodular and log-supermodular games given affiliated types,and in games with independent types in which each player's ex post payoff satisfies supermodularity in own action and nondecreasing differences in own action and type. This result is applied to provide the first proof of pure strategy equilibrium existence in the uniform price auction when bidders have multi-unit demand, nonprivate values, and independent types. Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 4 (07)
Pages: 1191-1214
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:4:p:1191-1214

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  1. Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  2. Philip J Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," Levine's Working Paper Archive 784828000000000413, David K. Levine. [Downloadable!]
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  3. Mathevet, Laurent, . "A contraction principle for finite global games," Working Papers 1243, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  4. Olivier Armantier & Jean-Pierre Florens & Jean-Francois Richard, 2008. "Approximation of Nash equilibria in Bayesian games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 965-981. [Downloadable!]
  5. LOVO, Stefano & ALBANO, Gian Luigi & GERMANO, Fabrizio, 2002. "On some collusive and signaling equilibria in ascending auctions for multiple objects," Les Cahiers de Recherche 765, HEC Paris. [Downloadable!]
  6. Christian Ewerhart & Nuno Cassola & Natacha Valla, 2006. "Declining valuations and equilibrium bidding in central bank refinancing operations," Working Paper Series 668, European Central Bank. [Downloadable!]
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  7. Aloisio Araujo & Luciano I. de Castro, 2006. "Pure Strategy Equilibria Of Single And Double Auctions With Interdependent Values," Economics Working Papers we065320, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  8. Mason, Robin & Valentinyi, Ãkos, 2003. "Independence And Heterogeneity In Games Of Incomplete Information," Discussion Paper Series In Economics And Econometrics 0307, Economics Division, School of Social Sciences, University of Southampton. [Downloadable!]
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  9. Moreira, Humberto Luiz Ataide & Araújo, Aloísio Pessoa de & Castro Filho, Luciano I. de Castro Filho, 2004. "Pure strategy equilibria of multidimensional and Non-monotonic auctions," Economics Working Papers (Ensaios Economicos da EPGE) 571, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
  10. 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. [Downloadable!]
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