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Supermodularity and complementarity in economics: an elementary survey

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  • AMIR, Rabah

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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Bibliographic 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: 00 Dec 2003
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Handle: RePEc:cor:louvco:2003104

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

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  1. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  2. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  3. Kyle Bagwell & Garey Ramey, 1995. "Coordination Economies," Discussion Papers 1148, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
  6. Martin Peitz, 1999. "- Aggregation In A Model Of Price Competition," Working Papers. Serie AD 1999-26, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. 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.
  8. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  9. Federico Echenique, 2001. "A characterization of strategic complementarities," Documentos de Trabajo (working papers) 0501, Department of Economics - dECON.
  10. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  11. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  12. Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Econometric Society World Congress 2000 Contributed Papers 1906, Econometric Society.
  13. 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.
  14. 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.
  15. Federico Echenique, 2000. "Mixed Equilibria in Games of Strategic Complementarities," Game Theory and Information 0004006, EconWPA.
  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.
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  18. Federico Echenique & Aaron Edlin, 2001. "Mixed Equilibria in Games of Strategic Complements are Unstable," Levine's Working Paper Archive 563824000000000161, David K. Levine.
  19. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  20. 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.
  21. 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.
  22. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  23. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  24. 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).
  25. 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..
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  29. 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.
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