The Re fined Best-Response Correspondence in Normal Form Games

22 Pages Posted: 23 Apr 2012

See all articles by Dieter Balkenborg

Dieter Balkenborg

University of Exeter - Department of Economics

Josef Hofbauer

University of Vienna - Department of Mathematics

Christoph Kuzmics

University of Graz - Department of Economics

Date Written: April 23, 2012

Abstract

This paper provides an in-depth study of the (most) refined best reply correspondence introduced by Balkenborg, Hofbauer, and Kuzmics (2012). An example demonstrates that this correspondence can be very different from the standard best reply correspondence. In two-player games, however, the refined best reply correspondence of a given game is the same as the best reply correspondence of a slightly modified game. The modified game is derived from the original game by reducing the payoff by a small amount for all pure strategies that are weakly inferior. Weakly inferior strategies, for two-player games, are pure strategies that are either weakly dominated or are equivalent to a proper mixture of other pure strategies. Fixed points of the refined best reply correspondence are not equivalent to any known Nash equilibrium refinement. A class of simple communication games demonstrates the usefulness and intuitive appeal of the refined best reply correspondence.

Keywords: best-response correspondence, persistent equilibria, Nash equilibrium refi nements, strict and weak dominance, strategic stability

JEL Classification: C62, C72, C73

Suggested Citation

Balkenborg, Dieter and Hofbauer, Josef and Kuzmics, Christoph, The Re fined Best-Response Correspondence in Normal Form Games (April 23, 2012). Institute of Mathematical Economics Working Paper, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2044819 or http://dx.doi.org/10.2139/ssrn.2044819

Dieter Balkenborg

University of Exeter - Department of Economics ( email )

Streatham Court
Exeter EX4 4PU
United Kingdom

Josef Hofbauer

University of Vienna - Department of Mathematics ( email )

Oskar-Morgenstern-Platz 1
A-1090 Vienna
Austria

Christoph Kuzmics (Contact Author)

University of Graz - Department of Economics ( email )

Universitaetsstrasse 15
RESOWI - F4
Graz, 8010
Austria

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