Pure strategy equilibria in symmetric two-player zero-sum games - Dürsch, Peter; Oechssler, Joerg; Schipper, Burkhard (International journal of game theory, 2012)
We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every ﬁnite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufﬁcient conditions for existence are provided. Our ﬁndings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric twoplayer zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of ﬁnite population evolutionary stable strategies.
Gesehen am 29.11.2018
First online: 15 September 2011