Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games

Francesco Caruso (francesco.caruso@unina.it), Maria Carmela Ceparano and Jacqueline Morgan
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Francesco Caruso: Università di Napoli Federico II

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: 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.

Keywords: Non-cooperative game; weighted potential game; uniqueness of Nash equilibrium; fixed point. (search for similar items in EconPapers)
Date: 2017-04-18, Revised 2017-06-18
New Economics Papers: this item is included in nep-gth and nep-mic
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Citations: View citations in EconPapers (2)

Published in Journal of Mathematical Analysis and Applications, 2018, 459(2), pp. 1208-1221

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