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Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games

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The literature results about existence of Nash equilibria in continuous potential games (Monderer and Shapley, 1996) exploits the property that any maximum point of the potential function is a Nash equilibrium of the game (the vice versa being not true) and those about uniqueness use strict concavity of the potential function. Therefore, the following question arises: can we find sufficient conditions on the data of the game which guarantee one and only one Nash equilibrium when existence of a maximum of the potential function is not ensured and the potential function in not strictly concave? The paper positively answers this question for two-player weighted potential games when the strategy sets are not bounded sets of not necessarily finite dimensional spaces. Significative examples infinite dimensional spaces are provided, together with an application in infinite dimensional ones.

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Paper provided by Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy in its series CSEF Working Papers with number 471.

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Date of creation: 18 Apr 2017
Date of revision: 18 Jun 2017
Handle: RePEc:sef:csefwp:471
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  1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293, December.
  2. repec:eee:mateco:v:70:y:2017:i:c:p:154-165 is not listed on IDEAS
  3. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters,in: Real Analysis with Economic Applications Princeton University Press.
  4. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, December.
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