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Nash equilibria of games with monotonic best replies

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  • Filippo L. Calciano

Abstract

We introduce notions of increasingness for the best reply of a game that capture properly the intuitive idea of complementarity among players’ strategies. We show, by generalizing the fixpoint theorems of Veinott and Zhou, that the Nash sets of our games with increasing best replies are nonempty complete lattices. Hence we extend the class of games with strategic complementarities.

Suggested Citation

  • Filippo L. Calciano, 2009. "Nash equilibria of games with monotonic best replies," Departmental Working Papers of Economics - University 'Roma Tre' 0108, Department of Economics - University Roma Tre.
  • Handle: RePEc:rtr:wpaper:0108
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    File URL: http://host.uniroma3.it/dipartimenti/economia/pdf/WP108.pdf
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    References listed on IDEAS

    as
    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Filippo L., CALCIANO, 2007. "Games with Complementarities," Discussion Papers (ECON - Département des Sciences Economiques) 2007011, Université catholique de Louvain, Département des Sciences Economiques.
    3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    4. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    5. Vives, Xavier, 2004. "Complementarities and Games: New Developments," CEPR Discussion Papers 4742, C.E.P.R. Discussion Papers.
    6. Elena Antoniadou, 2007. "Comparative Statics for the Consumer Problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 189-203, April.
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    More about this item

    Keywords

    Complementarity; supermodular games; fixpoint theorem; Nash equilibria;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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