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Reexamination of the perfectness concept for equilibrium points in extensive games

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  • Selten, Reinhard

    (Center for Mathematical Economics, Bielefeld University)

Abstract

The concept of a perfect equilibrium point has been introduced in order to exclude the possibility that disequilibrium behavior is prescribed on unreached subgames. (Selten 1965 and 1973). Unfortunately this definition of perfectness does not remove all difficulties which may arise with respect to unreached parts of the game. It is necessary to reexamine the problem of defining a satisfactory non-cooperative equilibrium concept for games in extensive form. Therefore a new concept of a perfect equilibrium point will be introduced in this paper. In retrospect the earlier use of the word "perfect" was premature. Therefore a perfect equilibrium point in the old Sense will be called "subgame perfect". The new definition of perfectness has the property that a perfect equilibrium point is always subgame perfect but a subgame perfect equilibrium point may not be perfect. It will be shown that every finite extensive game with perfect recall has at least one perfect equilibrium point. Since subgame perfectness cannot be detected in the normal form, it is clear that for the purpose of the investigation of the problem of perfectness, the normal form is an inadequate representation of the extensive form. It will be convenient to introduce an "agent normal form" as a more adequate representation of games with perfect recall.
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Suggested Citation

  • Selten, Reinhard, 2017. "Reexamination of the perfectness concept for equilibrium points in extensive games," Center for Mathematical Economics Working Papers 23, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:23
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    File URL: https://pub.uni-bielefeld.de/download/2909636/2911214
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    Cited by:

    1. Gleen W. Harrison & Jack Hirschleifer, 1985. "The Provision of Public Goods Under Alternative Protocols and Social Composition Functions: Report on an Experiment," UCLA Economics Working Papers 372, UCLA Department of Economics.
    2. White, Halbert & Xu, Haiqing & Chalak, Karim, 2014. "Causal discourse in a game of incomplete information," Journal of Econometrics, Elsevier, vol. 182(1), pages 45-58.
    3. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20 World Scientific Publishing Co. Pte. Ltd..
    4. Drew Fudenberg & David M. Kreps & David K. Levine, 2008. "On the Robustness of Equilibrium Refinements," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 5, pages 67-93 World Scientific Publishing Co. Pte. Ltd..
    5. Martin Shubik, 2007. "The Theory of Money and Financial Institutions: A Summary of a Game Theoretic Approach," The IUP Journal of Monetary Economics, IUP Publications, vol. 0(2), pages 6-26, May.
    6. Zame, William R, 1993. "Efficiency and the Role of Default When Security Markets Are Incomplete," American Economic Review, American Economic Association, vol. 83(5), pages 1142-1164, December.
    7. Jack Hirshleifer, 1985. "Protocol, Payoff, and Equilibrium: Game Theory and Social Modelling," UCLA Economics Working Papers 366, UCLA Department of Economics.
    8. Yves Breitmoser, 2012. "Proto-coalition bargaining and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 581-599, November.
    9. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    10. Michael Waldman, 1984. "Job Assignments, Signalling, and Efficiency," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 255-267, Summer.
    11. Georg Meran & Christian Hirschhausen, 2009. "A modified yardstick competition mechanism," Journal of Regulatory Economics, Springer, vol. 35(3), pages 223-245, June.
    12. Harrison, Glenn W & Hirshleifer, Jack, 1989. "An Experimental Evaluation of Weakest Link/Best Shot Models of Public Goods," Journal of Political Economy, University of Chicago Press, vol. 97(1), pages 201-225, February.
    13. Werner Güth, 2002. "On the Inconsistency of Equilibrium Refinement," Theory and Decision, Springer, vol. 53(4), pages 371-392, December.
    14. Michael Waldman, 1984. "The Role of Integrity in Economic Interaction," UCLA Economics Working Papers 350, UCLA Department of Economics.

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