Quadratic stochastic operators and zero-sum game dynamics - Ganikhodjaev, Nasir; Ganikhodjaev, Rasul; Jamilov, Uygun (Cambridge University Press, 2015)
In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex S4 and show that such operators can be reinterpreted in terms of zero-sum games. We show that an extremal Volterra operator is non-ergodic and an appropriate zero-sum game is a rock-paper-scissors game if either the Volterra operator is a uniform operator or for a non-uniform Volterra operator V there exists a subset I⊂{1,2,3,4,5} with |I|⩽2 such that ∑i∈I(Vnx)i→0, and the restriction of V on an invariant face ΓI={x∈Sm−1:xi=0,i∈I} is a uniform Volterra operator.