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Playing Multiple Complementarity Games Simultaneously

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  • Kiminori Matsuyama

Abstract

This paper analyzes the situation, in which a continuum of identical players is engaged in more than one activity and each activity is characterized by a complementarity game. The player's intensity levels across different activities are linked in such a way that the marginal cost of increasing her intensity in one activity increases with her own intensity levels in other activities. Compared to the case where these games are played independently, a smaller degree of complementarity in each game is required to generate multiple stable Nash equilibria, which are all asymmetric in that the players operate at different levels in different activities. The implications of these and other results, which have a close connection with the Frobenius theory of positive matrices, are discussed in the context of two macroeconomic applications: endogenous inequality of nations and endogenous business cycles.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1240.

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Date of creation: Jan 1999
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Handle: RePEc:nwu:cmsems:1240

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Related research

Keywords: Strategic Complementarities; Multiple Activities; Bifurcation Analysis; The Structure of the Equilibrium Set; Globalization and Inequality of Nations; Intertemporal Substitution and Business Cycles;

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References

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  1. Krugman, Paul & Venables, Anthony J., 1994. "Globalization and the Inequality of Nations," CEPR Discussion Papers 1015, C.E.P.R. Discussion Papers.
  2. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  3. Shleifer, Andrei, 1986. "Implementation Cycles," Scholarly Articles 3451303, Harvard University Department of Economics.
  4. Gertler, Mark & Rogoff, Kenneth, 1990. "North-South lending and endogenous domestic capital market inefficiencies," Journal of Monetary Economics, Elsevier, vol. 26(2), pages 245-266, October.
  5. Alwyn Young, 1991. "Learning by Doing and the Dynamic Effects of International Trade," NBER Working Papers 3577, National Bureau of Economic Research, Inc.
  6. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  7. Kiminori Matsuyama, 1990. "Agricultural Productivity, Comparative Advantage, and Economic Growth," Discussion Papers 934, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Raymond Deneckere & Kenneth Judd, 1986. "Cyclical and Chaotic Behavior in a Dynamic Equilibrium Model," Discussion Papers 734, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Holmstrom, Bengt & Milgrom, Paul, 1991. "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design," Journal of Law, Economics and Organization, Oxford University Press, vol. 7(0), pages 24-52, Special I.
  10. Gale, Douglas, 1996. "Delay and Cycles," Review of Economic Studies, Wiley Blackwell, vol. 63(2), pages 169-98, April.
  11. Kiminori Matsuyama, 1990. "Increasing Returns, Industrialization and Indeterminacy of Equilibrium," Discussion Papers 878, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  13. Krugman, Paul, 1981. "Trade, accumulation, and uneven development," Journal of Development Economics, Elsevier, vol. 8(2), pages 149-161, April.
  14. Kiminori Matsuyama, 1999. "Growing Through Cycles," Econometrica, Econometric Society, vol. 67(2), pages 335-348, March.
  15. Herrendorf, B. & Valentinyi, A. & Waldmann, R., 1998. "Ruling out indeterminacy: the role of heterogeneity," Discussion Paper Series In Economics And Econometrics 9803, Economics Division, School of Social Sciences, University of Southampton.
  16. Fudenberg, Drew & Diamond, Peter, 1989. "Rational Expectations Business Cycles in Search Equilibrium," Scholarly Articles 3374509, Harvard University Department of Economics.
  17. Murphy, Kevin M & Shleifer, Andrei & Vishny, Robert W, 1989. "Industrialization and the Big Push," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1003-26, October.
  18. Russell Cooper & John Haltiwanger, 1990. "Macroeconomic Implications of Production Bunching: Factor Demand Linkages," Papers 0001, Boston University - Industry Studies Programme.
  19. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 441-63, August.
  20. repec:fth:iniesr:430 is not listed on IDEAS
  21. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
  22. Herrendorf, Berthold & Valentinyi, Akos & Waldmann, Robert, 2000. "Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 295-307, April.
  23. Goyal, Sanjeev & Janssen, Maarten C. W., 1997. "Non-Exclusive Conventions and Social Coordination," Journal of Economic Theory, Elsevier, vol. 77(1), pages 34-57, November.
  24. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
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Cited by:
  1. Kiminori Matsuyama, 2002. "Explaining Diversity: Symmetry-Breaking in Complementarity Games," Discussion Papers 1336, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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