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Playing Multiple Complementarity Games Simultaneously

  • Kiminori Matsuyama

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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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
Contact details of provider: 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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  1. Kevin M. Murphy & Andrei Shleifer & Robert W. Vishny, 1988. "Industrialization and the Big Push," NBER Working Papers 2708, National Bureau of Economic Research, Inc.
  2. Russell Cooper & John Haltiwanger, 1990. "Macroeconomic Implications of Production Bunching: Factor Demand Linkages," Papers 0001, Boston University - Industry Studies Programme.
  3. Kiminori Matsuyama, 1990. "Agricultural Productivity, Comparative Advantage, and Economic Growth," Discussion Papers 934, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
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  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. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Matsuyama, Kiminori, 1996. "Growing Through Cycles," Economics Series 40, Institute for Advanced Studies.
  11. 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.
  12. Diamond, Peter & Fudenberg, Drew, 1989. "Rational Expectations Business Cycles in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 606-19, June.
  13. Alwyn Young, 1991. "Learning by Doing and the Dynamic Effects of International Trade," NBER Working Papers 3577, National Bureau of Economic Research, Inc.
  14. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  15. 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.
  16. 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.
  17. Shleifer, Andrei, 1986. "Implementation Cycles," Scholarly Articles 3451303, Harvard University Department of Economics.
  18. 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.
  19. Krugman, Paul, 1981. "Trade, accumulation, and uneven development," Journal of Development Economics, Elsevier, vol. 8(2), pages 149-161, April.
  20. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May.
  21. Herrendorf, Berthold & Valentinyi, Akos & Waldmann, Robert, 1998. "Ruling out Indeterminacy: the Role of Heterogeneity," CEPR Discussion Papers 1858, C.E.P.R. Discussion Papers.
  22. Gale, Douglas, 1996. "Delay and Cycles," Review of Economic Studies, Wiley Blackwell, vol. 63(2), pages 169-98, April.
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