Nash equilibria of games with increasing best replies
AbstractThe intuitive idea of two activities being complements, for example tea and lemon, is that increasing the level of one makes somehow desirable to increase the level of the other (Samuelson, 1974). Hence complementarity, in its very nature, is a sensitivity property of the set of solutions to an optimization problem. In the context of games, complementarity should then be captured by properties of the joint best reply. We introduce notions of increasingness for the joint best reply which capture properly this intuitive idea of complementarity among players’ strategies. We show, by generalizing the fixpoint theorems of Veinott (1992) and Zhou (1994), that the Nash sets of our games are nonempty complete lattices. Hence we extend the class of games with strategic complementarities
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009082.
Date of creation: 01 Dec 2009
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strategic complementarity; supermodular games; quasisupermodular games; fixpoint theorem; Nash equilibria;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-28 (All new papers)
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- 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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