Nash equilibrium uniqueness in nice games with isotone best replies

Maria Carmela Ceparano and Federico Quartieri

MPRA Paper from University Library of Munich, Germany

Abstract: We prove the existence of a unique pure-strategy Nash equilibrium in nice games with isotone chain-concave best replies and compact strategy sets. We establish a preliminary fixpoint uniqueness argument, thus showing sufficient assumptions on the best replies of a nice game that guarantee the existence of exactly one Nash equilibrium. Then, by means of a comparative statics analysis, we examine the necessity and sufficiency of the conditions on marginal utility functions for such assumptions to be satisfied; in particular, we find necessary and sufficient conditions for the isotonicity and chain-concavity of best replies. We extend the results on Nash equilibrium uniqueness to nice games with upper unbounded strategy sets and we present "dual" results for games with isotone chain-convex best replies. A final application to Bayesian games is exhibited.

Keywords: Nash equilibrium uniqueness; Chain-concave best reply; Nice game; Comparative statics; Strategic complementarity. (search for similar items in EconPapers)
JEL-codes: C61 C72 (search for similar items in EconPapers)
Date: 2015-10-05, Revised 2016-01-24
New Economics Papers: this item is included in nep-gth and nep-hpe
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Related works:
Journal Article: Nash equilibrium uniqueness in nice games with isotone best replies (2017)
Working Paper: Nash equilibrium uniqueness in nice games with isotone best replies (2015)
Working Paper: Nash equilibrium uniqueness in nice games with isotone best replies (2015)
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