Summary
In this paper attention is focussed on the structure of the set of perfect equilibria. It turns out that the structure of this set resembles the structure of the Nash equilibrium set. Maximal Selten subsets are introduced to take the role of maximal Nash subsets. It is found that the set of perfect equilibria is the finite union of maximal Selten subsets. Furthermore it is shown that the dimension relation for maximal Nash subsets can be extended to faces of such sets. As a result a dimension relation for maximal Selten subsets is derived.
Zusammenfassung
Die vorliegende Arbeit ist der Struktur der Menge perfekter Gleichgewichte gewidmet. Es stellt sich heraus, daß die Struktur dieser Menge der Struktur der Menge der Nash Gleichgewichte ähnlich ist. Maximale Selten Mengen werden eingeführt, um die Rolle der maximalen Nash Menge zu übernehmen. Es wird gezeigt, daß die Menge perfekter Gleichgewichte aus endlich vielen maximalen Selten Mengen zusammengestellt ist. Außerdem wird die Dimension maximaler Selten Mengen beschrieben.
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Borm, P.E.M., Jansen, M.J.M., Potters, J.A.M. et al. On the structure of the set of perfect equilibria in bimatrix games. OR Spektrum 15, 17–20 (1993). https://doi.org/10.1007/BF01783413
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DOI: https://doi.org/10.1007/BF01783413