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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. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  2. 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.
  3. Federico Echenique, 2000. "Mixed Equilibria in Games of Strategic Complementarities," Game Theory and Information 0004006, EconWPA.
  4. 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.
  5. 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..
  6. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  7. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
  8. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  9. Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
  10. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  11. 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.
  12. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  13. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  14. 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).
  15. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  16. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  17. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
  18. Kyle Bagwell & Garey Ramey, 1995. "Coordination Economies," Discussion Papers 1148, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  19. 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.
  20. 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.
  21. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society.
  22. 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.
  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. 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).
  25. 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.
  26. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  27. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  28. Martin Peitz, 1999. "- Aggregation In A Model Of Price Competition," Working Papers. Serie AD 1999-26, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  29. 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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