Summary.
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.
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Received: 22 September 2003, Revised: 31 March 2004,
JEL Classification Numbers:
C72, D00, D40.
Correspondence to: Robert A. Becker
We have benefited from comments on an earlier draft made by participants at Indiana University’s Microeconomics workshop (October 2002) and the Midwest Economic Theory Conference held at the University of Pittsburgh (May 2003). We also thank Roy Gardner for comments on earlier versions. We thank the Associate Editor, Mark Machina, for his detailed comments and suggestions. This project began when Subir Chakrabarti was a visitor in the Department of Economics, Indiana University, Bloomington in the Spring of 2002. He thanks that department for its support.
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Becker, R.A., Chakrabarti, S.K. Satisficing behavior, Brouwer’s Fixed Point Theorem and Nash Equilibrium. Economic Theory 26, 63–83 (2005). https://doi.org/10.1007/s00199-004-0519-z
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DOI: https://doi.org/10.1007/s00199-004-0519-z