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Games with Complementarities

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  • Filippo L., CALCIANO

Abstract

We introduce a class of games with complementarities that has the quasisupermodular games, hence the supermodular games, as a special case. Our games retain the main property of quasisupermodular games : the Nash set is a nonemply complete lattice. We use monotonicity properties on the best reply that are weaker than those in the literature, as well as pretty simple and linked with an intuitive idea of complementarity. The sufficient conditions on the payoffs are weaker than those in quasisupermodular games. We also separate the conditions implying existence of a greatest and a least Nash equilibrium from those, stronger, implying that the Nash set is a complete lattice

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Bibliographic Info

Paper provided by Université catholique de Louvain, Département des Sciences Economiques in its series Discussion Papers (ECON - Département des Sciences Economiques) with number 2007011.

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Length: 31
Date of creation: 01 Mar 2007
Date of revision:
Handle: RePEc:ctl:louvec:2007011

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Keywords: Complementarity; Quasisupermodularity; Supermodular games; Monotone comparative statics; Nash equilibria;

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References

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  1. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  2. 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.
  3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  4. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-89, December.
  5. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
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Cited by:
  1. 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.
  2. CALCIANO, Filippo L., 2011. "Oligopolistic competition with general complementarities," CORE Discussion Papers 2011054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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