The Refined Best-Response Correspondence in Normal Form Games
University of Exeter - Department of Economics
University of Vienna - Department of Mathematics
April 23, 2012
Institute of Mathematical Economics Working Paper, Forthcoming
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.
Number of Pages in PDF File: 22
Keywords: best-response correspondence, persistent equilibria, Nash equilibrium refinements, strict and weak dominance, strategic stability
JEL Classification: C62, C72, C73working papers series
Date posted: April 23, 2012
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