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The refined best-response correspondence in normal form games

  • 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)

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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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics 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
Contact details of provider: Postal: Postfach 10 01 31, 33501 Bielefeld
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  1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  2. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "Fictitious Play in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 177-202, August.
  3. Kuzmics, Christoph & Balkenborg, Dieter & Hofbauer, Josef, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
  4. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
  5. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
  6. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  7. Jansen, M.J.M. & Jurg, A.P. & Borm, P.E.M., 1994. "On strictly perfect sets," Other publications TiSEM 77ebc80c-ac78-43a0-808b-6, Tilburg University, School of Economics and Management.
  8. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008. "Admissibility in Games," Econometrica, Econometric Society, vol. 76(2), pages 307-352, 03.
  9. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, July.
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