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Monotonicity of Solution Sets for Parameterized Optimization Problems

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  • Leslie M. Marx

Abstract

This paper uses results of lattice theory, convex analysis, and nonsmooth analysis to establish conditions for the existence of pure-strategy Nash equilibria when payoff functions are continuous but not quasi-concave. A class of economic games for which this theory is important is given.

Suggested Citation

  • Leslie M. Marx, 1991. "Monotonicity of Solution Sets for Parameterized Optimization Problems," Discussion Papers 1067, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1067
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    References listed on IDEAS

    as
    1. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    4. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-528, June.
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