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Supermodularity and Complementarity in Economics: An Elementary Survey

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  • Rabah Amir

    ()
    (Department of Economics, University of Arizona)

Abstract

The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities. The results are presented in a simplified yet rigourous manner, without reference to lattice theory, for the special case of one-dimensional parameter and actions sets, with the emphasis being on wide accessibility. Detailed applications are presented for well-known models of consumer behavior, monopoly pass-through, Bertrand and Cournot competition, strategic R&D, search, and matching. Wherever appropriate, useful tricks for applications and comparative comments are inserted.

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Bibliographic Info

Article provided by Southern Economic Association in its journal Southern Economic Journal.

Volume (Year): 71 (2005)
Issue (Month): 3 (January)
Pages: 636-660

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Handle: RePEc:sej:ancoec:v:71:3:y:2005:p:636-660

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Web page: http://www.southerneconomic.org/
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  1. 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).
  2. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society.
  3. Echenique, Federico, 2002. "A Characterization of Strategic Complementarities," Working Papers 1142, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  6. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  7. Federico Echenique & Aaron Edlin, 2003. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Game Theory and Information 0303003, EconWPA.
  8. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  9. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  10. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  11. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
  12. Federico Echenique, 1999. "Comparative Statics by Adaptative Dynamics and the Correspondence Principle," Documentos de Trabajo (working papers) 2099, Department of Economics - dECON.
  13. Federico Echenique, 2003. "Mixed equilibria in games of strategic complementarities," Economic Theory, Springer, vol. 22(1), pages 33-44, 08.
  14. Peitz, Martin, 2000. "Aggregation in a Model of Price Competition," Journal of Economic Theory, Elsevier, vol. 90(1), pages 1-38, January.
  15. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x.
  16. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  17. Amir, Rabah & Wooders, John, 1997. "One-Way Spillovers, Endogenous Innovator/Imitator Roles and Research Joint Ventures," Economics Series 43, Institute for Advanced Studies.
  18. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
  19. Kyle Bagwell & Garey Ramey, 1992. "Coordination Economies," Discussion Papers 1034, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Milgrom, Paul & Roberts, John, 1995. "Complementarities and fit strategy, structure, and organizational change in manufacturing," Journal of Accounting and Economics, Elsevier, vol. 19(2-3), pages 179-208, April.
  21. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  22. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  23. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  24. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  25. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  26. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  27. Friedman, Eric J. & Johnson, Simon, 1997. "Dynamic Monotonicity and Comparative Statics for Real Options," Journal of Economic Theory, Elsevier, vol. 75(1), pages 104-121, July.
  28. 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.
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