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Games with Strategic Heterogeneity

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  • Andrew Monaco

    (Department of Economics, Colgate University)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

Abstract

This paper studies games with both strategic substitutes and strategic complements, and more generally, games with strategic heterogeneity (GSH). Such games may behave differ- ently from either games with strategic complements or games with strategic substitutes. Under mild assumptions (on one or two players only), the equilibrium set in a GSH is totally unordered (no two equilibria are comparable in the standard product order). Moreover, under mild assumptions (on one player only), parameterized GSH do not allow decreasing equilibrium selections. In general, this cannot be strengthened to conclude in- creasing selections. Monotone comparative statics results are presented for games in which some players exhibit strategic substitutes and others exhibit strategic complements. For two-player games with linearly ordered strategy spaces, there is a characterization. More generally, there are sufficient conditions. The conditions apply only to players exhibiting strategic substitutes; no conditions are needed for players with strategic complements. Several examples highlight the results.

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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201240.

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Length: 42 pages
Date of creation: Nov 2012
Date of revision: Nov 2012
Handle: RePEc:kan:wpaper:201240

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Related research

Keywords: Lattice games; strategic complements; strategic substitutes; strategic hetergeneity; equilibrium set; monotone comparative statics;

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  1. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 93(3), pages 488-511, June.
  2. Roy, Sunanda & Sabarwal, Tarun, 2006. "On the (non-)lattice structure of the equilibrium set in games with strategic substitutes," MPRA Paper 4120, University Library of Munich, Germany, revised 23 May 2007.
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  15. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1255-77, November.
  16. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, Elsevier, vol. 7(2), pages 295-300, September.
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  18. AMIR, Rabah, 1994. "Cournot Oligopoly and the Theory of Supermodular Games," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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