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Supermodularity and complementarity in economics: an elementary survey

  • AMIR, Rabah

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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number 1823.

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Handle: RePEc:cor:louvrp:1823
Note: In : Southern Economic Journal, 71(3), 636-660, 2005
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  2. 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.
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  8. 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..
  9. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
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  12. Amir, R., . "Sensitivity analysis of multisector optimal economic dynamics," CORE Discussion Papers RP 1192, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. AMIR, Rabah & GRILO, Isabel, . "Stackelberg versus Cournot equilibrium," CORE Discussion Papers RP 1368, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  15. AMIR, Rabah & LAMBSON, Val, 1999. "On the effects of entry in Cournot markets," CORE Discussion Papers 1999059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Kyle Bagwell & Garey Ramey, 1992. "Coordination Economies," Discussion Papers 1034, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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.
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  20. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  21. 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.
  22. Amir, Rabah & Wooders, John, 2000. "One-Way Spillovers, Endogenous Innovator/Imitator Roles, and Research Joint Ventures," Games and Economic Behavior, Elsevier, vol. 31(1), pages 1-25, April.
  23. 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.
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  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967, November.
  30. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
  31. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521570176, November.
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