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The refined best-response correspondence in normal form games

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Author Info

  • Dieter Balkenborg

    (Department of Economics, School of Business and Economics, University of Exeter)

  • Josef Hofbauer

    (Department of Mathematics, University of Vienna)

  • Christoph Kuzmics

    (Bielefeld University)

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.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-466.pdf
File Function: First version, 2012
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 466.

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Length: 22 pages
Date of creation: Apr 2012
Date of revision:
Handle: RePEc:bie:wpaper:466

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  1. Jansen M. J. M. & Jurg A. P. & Borm P. E. M., 1994. "On Strictly Perfect Sets," Games and Economic Behavior, Elsevier, vol. 6(3), pages 400-415, May.
  2. Kuzmics, Christoph & Balkenborg, Dieter & Hofbauer, Josef, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
  3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
  4. Ebbe Hendon & Hans Jørgen Jacobsen & Birgitte Sloth, . "Fictitious Play in Extensive Form Games," Discussion Papers 94-06, University of Copenhagen. Department of Economics.
  5. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
  6. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  7. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
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Cited by:
  1. Kuzmics, Christoph & Balkenborg, Dieter & Hofbauer, Josef, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
  2. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2011. "Refined best reply correspondence and dynamics," Working Papers 451, Bielefeld University, Center for Mathematical Economics.

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