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Supermodularity and Complementarity in Economics: An Elementary Survey

  • Rabah Amir

    ()

    (Department of Economics, University of Arizona)

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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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
Contact details of provider: Web page: http://www.southerneconomic.org/

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  1. Rabah Amir & John Wooders, 1998. "One-Way Spillovers, Endogenous Innovator/Imitator Roles and Research Jointventures," CIE Discussion Papers 1998-10, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
  2. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  3. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. 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.
  5. Echenique, Federico & Edlin, Aaron S., 2002. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Competition Policy Center, Working Paper Series qt2b85c93d, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
  6. 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.
  7. Federico Echenique, 2000. "Mixed Equilibria in Games of Strategic Complementarities," Game Theory and Information 0004006, EconWPA.
  8. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967, September.
  9. Kyle Bagwell & Garey Ramey, 1995. "Coordination Economies," Discussion Papers 1148, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
  11. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  12. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  13. Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
  14. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  15. Rabah Amir & Val E. Lambson, 2000. "On the Effects of Entry in Cournot Markets," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 235-254.
  16. Hoernig, Steffen H., 2003. "Existence of equilibrium and comparative statics in differentiated goods Cournot oligopolies," International Journal of Industrial Organization, Elsevier, vol. 21(7), pages 989-1019, September.
  17. Peitz, Martin, 2000. "Aggregation in a Model of Price Competition," Journal of Economic Theory, Elsevier, vol. 90(1), pages 1-38, January.
  18. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  19. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  20. 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..
  21. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521570176, September.
  22. 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).
  23. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, March.
  24. 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.
  25. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  26. 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.
  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. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  29. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
  30. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-27, March.
  31. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
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