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- W1986168457 abstract "In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex $S^{4}$ 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 $Isubset {1,2,3,4,5}$ with $|I|leq 2$ such that $sum _{iin I}(V^{n}mathbf{x})_{i}rightarrow 0,$ and the restriction of $V$ on an invariant face ${rmGamma}_{I}={mathbf{x}in S^{m-1}:x_{i}=0,iin I}$ is a uniform Volterra operator." @default.
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- W1986168457 date "2014-06-20" @default.
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- W1986168457 title "Quadratic stochastic operators and zero-sum game dynamics" @default.
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- W1986168457 doi "https://doi.org/10.1017/etds.2013.109" @default.
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