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Supermodularity and complementarity in ecnomics: an elementary survey

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Author Info
AMIR, Rabah

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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 onedimensional parameter and actions sets, with the emphasis being onwide 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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Publisher Info
Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2003104.

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Date of creation: 01 Dec 2003
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Handle: RePEc:cor:louvco:2003104

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Related research
Keywords: complementarity; supermodularity; comparative statics; ordinal/cardinal; strategic complementarity; oligopoly;

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Find related papers by JEL classification:
A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. 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. [Downloadable!] (restricted)
  2. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society. [Downloadable!]
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  3. Kyle Bagwell & Garey Ramey, 1992. "Coordination Economies," Discussion Papers 1034, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  4. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Blackwell Publishing, vol. 52(1), pages 85-98, January. [Downloadable!] (restricted)
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  5. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January. [Downloadable!] (restricted)
  6. Federico Echenique, 2001. "A Characterization of Strategic Complementarities," Department of Economics, Working Paper Series 1020, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
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  7. 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. [Downloadable!] (restricted)
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  8. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February. [Downloadable!] (restricted)
  9. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  10. 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. [Downloadable!] (restricted)
  11. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  12. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March. [Downloadable!] (restricted)
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  13. 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.. [Downloadable!] (restricted)
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  14. Peitz, Martin, 2000. "Aggregation in a Model of Price Competition," Journal of Economic Theory, Elsevier, vol. 90(1), pages 1-38, January. [Downloadable!] (restricted)
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  15. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
  17. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March. [Downloadable!] (restricted)
  18. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  19. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141. [Downloadable!] (restricted)
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  20. 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. [Downloadable!] (restricted)
  21. Federico Echenique & Aaron Edlin, 2001. "Mixed Equilibria in Games of Strategic Complements are Unstable," Levine's Working Paper Archive 563824000000000161, David K. Levine. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Macedo, Jorge Braga de & Martins, Joaquim Oliveira, 2006. "Growth, Reform indicators and Policy complementarities," FEUNL Working Paper Series wp484, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
    Other versions:
  2. KNAUFF, Malgorzata, 2006. "Market transparency and Bertrand competition," CORE Discussion Papers 2006037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  3. Tabellini, Guido, 2007. "The Scope of Cooperation: Values and incentives," CEPR Discussion Papers 6534, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  4. Guido Tabellini, 2007. "The Scope of Cooperation: Norms and Incentives," Levine's Working Paper Archive 321307000000000866, David K. Levine. [Downloadable!]
  5. Sylvain Dessy & Jacques Ewoudou, 2006. "Microfinance and Female Empowerment," Cahiers de recherche 0603, CIRPEE. [Downloadable!]
  6. Harhoff, Dietmar & von Graevenitz, Georg & Wagner, Stefan, 2008. "Incidence and Growth of Patent Thickets - The Impact of Technological Opportunities and Complexity," CEPR Discussion Papers 6900, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  7. Van Essen, Matthew J., 2008. "A Simple Supermodular Mechanism that Implements Lindahl Allocations," MPRA Paper 12781, University Library of Munich, Germany. [Downloadable!]
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