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On The Kuhn Equivalence Of Strategies

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  • JOHN HILLAS
  • DMITRIY KVASOV

Abstract

We show that two strategies are Kuhn equivalent if and only if they induce the same probability measure over ter- minal nodes against some profile of completely mixed behaviour strategies of the other players. This result allows us to embed the equivalence classes of strategies in the probability measures over terminal nodes for various strategy concepts. This, in turn, allows a very clean statement of the relation between the various sets of strategies in games with perfect recall, linear games, and nonlin- ear games. It also proves useful in defining and analysing solution concepts in games without perfect recall, and, in particular, in nonlinear games.

Suggested Citation

  • John Hillas & Dmitriy Kvasov, 2021. "On The Kuhn Equivalence Of Strategies," Working Papers 2021, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2021
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    References listed on IDEAS

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    1. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    2. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    3. Hillas, John & Kvasov, Dmitriy, 2020. "Backward induction in games without perfect recall," Games and Economic Behavior, Elsevier, vol. 124(C), pages 207-218.
    4. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
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    Keywords

    extensive form games; perfect recall; linear games; non- linear games; Kuhn equivalence.;
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