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Games with Strategic Heterogeneity

  • Andrew Monaco

    (Department of Economics, Colgate University)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

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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File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201240.pdf
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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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  1. Tombak, Mihkel M., 2006. "Strategic asymmetry," Journal of Economic Behavior & Organization, Elsevier, vol. 61(3), pages 339-350, November.
  2. Gary S. Becker, 1968. "Crime and Punishment: An Economic Approach," Journal of Political Economy, University of Chicago Press, vol. 76, pages 169.
  3. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  4. 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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  9. Federico Echenique, 1999. "Comparative Statics by Adaptative Dynamics and the Correspondence Principle," Documentos de Trabajo (working papers) 2099, Department of Economics - dECON.
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  12. Acemoglu, Daron & Jensen, Martin Kaae, 2009. "Aggregate Comparative Statics," CEPR Discussion Papers 7254, C.E.P.R. Discussion Papers.
  13. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  14. Amir, Rabah & Garcia, Filomena & Knauff, Malgorzata, 2010. "Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1968-1986, September.
  15. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  16. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, 03.
  17. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
  18. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
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