Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions
Abstract
In this paper we constructively prove the existence of Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions by a constructive version of Kakutani's fixed point theorem for sequentially locally non-constant multi-functions (multi-valued functions or correspondences). We also examine the existence of Nash equilibrium in a game with continuous strategies and quasi-concave payoff functions which has sequentially locally at most one maximum. We follow the Bishop style constructive mathematics.
Copyright © 2012 Yasuhito Tanaka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
Y. Tanaka, Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions, Adv. Fixed Point Theory 2 (2012), 398–416.
BibTeX
@article{Tanaka2012,
author = {Tanaka, Yasuhito},
title = {Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions},
journal = {Adv. Fixed Point Theory},
volume = {2},
year = {2012},
pages = {398--416},
doi = {}
}