Games with Strategic Heterogeneity
AbstractThis 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 InfoPaper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201240.
Length: 42 pages
Date of creation: Nov 2012
Date of revision: Nov 2012
Lattice games; strategic complements; strategic substitutes; strategic hetergeneity; equilibrium set; monotone comparative statics;
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-06 (All new papers)
- NEP-COM-2012-12-06 (Industrial Competition)
- NEP-GTH-2012-12-06 (Game Theory)
- NEP-HPE-2012-12-06 (History & Philosophy of Economics)
- NEP-MIC-2012-12-06 (Microeconomics)
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- Vives, Xavier, 1990.
"Nash equilibrium with strategic complementarities,"
Journal of Mathematical Economics,
Elsevier, vol. 19(3), pages 305-321.
- Tombak, Mihkel M., 2006. "Strategic asymmetry," Journal of Economic Behavior & Organization, Elsevier, vol. 61(3), pages 339-350, November.
- Federico Echenique, 2002.
"Comparative Statics by Adaptive Dynamics and the Correspondence Principle,"
Econometric Society, vol. 70(2), pages 833-844, March.
- Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," GE, Growth, Math methods 9912002, EconWPA.
- Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
- Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Econometric Society World Congress 2000 Contributed Papers 1906, Econometric Society.
- Federico Echenique, 1999. "Comparative Statics by Adaptative Dynamics and the Correspondence Principle," Documentos de Trabajo (working papers) 2099, Department of Economics - dECON.
- John K.-H. Quah & Bruno Strulovici, 2007.
"Comparative Statics, Informativeness, and the Interval Dominance Order,"
2007-W04, Economics Group, Nuffield College, University of Oxford.
- John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
- John Quah & Bruno Strulovici, 2007. "Comparative Statics, Informativeness, and the Interval Dominance Order," Economics Series Working Papers 2007-WO4, University of Oxford, Department of Economics.
- AMIR, Rabah, 1994.
"Cournot Oligopoly and the Theory of Supermodular Games,"
CORE Discussion Papers
1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
- 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.
- Roy, Sunanda & Sabarwal, Tarun, 2006.
"On the (non-)lattice structure of the equilibrium set in games with strategic substitutes,"
4120, University Library of Munich, Germany, revised 23 May 2007.
- Sunanda Roy & Tarun Sabarwal, 2008. "On the (non-)lattice structure of the equilibrium set in games with strategic substitutes," Economic Theory, Springer, vol. 37(1), pages 161-169, October.
- John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, 03.
- Alexander Zimper, 2007.
"A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes,"
International Journal of Game Theory,
Springer, vol. 36(1), pages 107-117, September.
- Alexander Zimper, 2005. "A fixed point characterization of the dominancesolvability of lattice games with strategic substitutes," Working Papers 32, Economic Research Southern Africa.
- Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
- Edlin, Aaron S. & Shannon, Chris, 1998.
"Strict Monotonicity in Comparative Statics,"
Journal of Economic Theory,
Elsevier, vol. 81(1), pages 201-219, July.
- Acemoglu, Daron & Jensen, Martin Kaae, 2009.
"Aggregate Comparative Statics,"
CEPR Discussion Papers
7254, C.E.P.R. Discussion Papers.
- 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.
- Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-98, December.
- Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
- Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
- Gary S. Becker, 1974.
"Crime and Punishment: An Economic Approach,"
in: Essays in the Economics of Crime and Punishment, pages 1-54
National Bureau of Economic Research, Inc.
- Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
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