# Satisficing behavior, Brouwer’s Fixed Point Theorem and Nash Equilibrium

*Robert Becker* and
*Subir Chakrabarti* ()

*Economic Theory*, 2005, vol. 26, issue 1, 63-83

**Abstract:**
We show that Nash Equilibrium points can be obtained by using response maps or reply functions that simply use better responses rather than best responses. We demonstrate the existence of a Nash Equilibrium as the fixed point of a better response map and since the better response map is continuous the fixed point can be established by simply using Brouwer’s fixed point theorem. The proof applies to games with a finite number of strategies as well as to games with a continuum of strategies. In case the games have a continuum of strategies the payoff functions have to be continuous on the action sets and quasi concave on the player’s action set. Copyright Springer-Verlag Berlin/Heidelberg 2005

**Keywords:** Nash equilibrium; Satisficing behavior; Brouwer’s Fixed Point Theorem; Better responses; Best responses; Cournot duopoly; Weighted expected utility; Bimatrix games; n-person games. (search for similar items in EconPapers)

**Date:** 2005

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