The refined best-response correspondence in normal form games

Dieter Balkenborg, Josef Hofbauer and Christoph Kuzmics

International Journal of Game Theory, 2015, vol. 44, issue 1, 165-193

Abstract: This paper provides an in-depth study of the (most) refined best-response correspondence introduced by Balkenborg et al. (Theor Econ 8:165–192, 2013 ). An example demonstrates that this correspondence can be very different from the standard best-response correspondence. In two-player games, however, the refined best-response correspondence of a given game is the same as the best-response 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 pure strategies. Fixed points of the refined best-response 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-response correspondence. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Best-response correspondence; Persistent equilibria; Nash equilibrium refinements; Strict and weak dominance; Strategic stability; Fictitious play; C62; C72; C73 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Working Paper: The refined best-response correspondence in normal form games (2014)
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DOI: 10.1007/s00182-014-0424-z

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