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Nash equilibria of games with monotonic best replies

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  • Filippo L. Calciano
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    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.

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    File URL: http://host.uniroma3.it/dipartimenti/economia/pdf/WP108.pdf
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    Bibliographic Info

    Paper provided by Department of Economics - University Roma Tre in its series Departmental Working Papers of Economics - University 'Roma Tre' with number 0108.

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    Length: 14
    Date of creation: 2009
    Date of revision:
    Handle: RePEc:rtr:wpaper:0108

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    Related research

    Keywords: Complementarity; supermodular games; fixpoint theorem; Nash equilibria;

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    1. CALCIANO, Filippo L., 2007. "Games with complementarities," CORE Discussion Papers 2007016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Elena Antoniadou, 2007. "Comparative Statics for the Consumer Problem," Economic Theory, Springer, vol. 31(1), pages 189-203, April.
    3. 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.
    4. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
    5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
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