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Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games

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  • Reinhard Selten

    (Institute of 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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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-23a.pdf
File Function: First version, 1974
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 023.

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Length: 46 pages
Date of creation: Aug 1974
Date of revision:
Handle: RePEc:bie:wpaper:023

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