Nash equilibrium uniqueness in nice games with isotone best replies

Ceparano, Maria Carmela and Quartieri, Federico (2015): Nash equilibrium uniqueness in nice games with isotone best replies.

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 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Nash equilibrium uniqueness; Chain-concave best replies; Nice games; Comparative statics; Strategic complementarity.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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