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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.

Suggested Citation

  • Kiminori Matsuyama, 1999. "Playing Multiple Complementarity Games Simultaneously," Discussion Papers 1240, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1240
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1240.pdf
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    References listed on IDEAS

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    Cited by:

    1. Kiminori Matsuyama, 2002. "Explaining Diversity: Symmetry-Breaking in Complementarity Games," American Economic Review, American Economic Association, vol. 92(2), pages 241-246, May.

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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