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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 & Val E. Lambson, 1998. "On the Effects of Entry in Cournot Markets," CIE Discussion Papers 1998-06, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
  2. Amir, Rabah & Wooders, John, 1997. "One-Way Spillovers, Endogenous Innovator/Imitator Roles and Research Joint Ventures," Economics Series 43, Institute for Advanced Studies.
  3. Federico Echenique, 2000. "Mixed Equilibria in Games of Strategic Complementarities," Documentos de Trabajo (working papers) 1400, Department of Economics - dECON.
  4. Echenique, Federico, 2002. "A Characterization of Strategic Complementarities," Working Papers 1142, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Echenique, Federico & Edlin, Aaron S., 2002. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Department of Economics, Working Paper Series qt26r9r912, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  7. 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.
  8. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  9. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
  10. Peitz, Martin, 2000. "Aggregation in a Model of Price Competition," Journal of Economic Theory, Elsevier, vol. 90(1), pages 1-38, January.
  11. Kyle Bagwell & Garey Ramey, 1992. "Coordination Economies," Discussion Papers 1034, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  13. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521570176, june. pag.
  14. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
  15. Amir, R., 1991. "Sensitivity analysis of multi-sector optimal economic dynamics," CORE Discussion Papers 1991006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
  17. 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..
  18. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
  19. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967, june. pag.
  20. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
  21. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
  22. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  23. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  24. 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.
  25. 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.
  26. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  27. 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.
  28. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
  29. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  30. 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.
  31. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-27, March.
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