Non-ergodicity of uniform quadratic stochastic operators. (English) Zbl 1344.37093

Summary: In this paper we consider a uniform extremal Volterra quadratic stochastic operator defined on an even-dimensional unit simplex, which corresponds to a balanced digraph, and show that such operator has the non-ergodicity property. We also reinterpret this result in the framework of zero-sum games obtaining that these operators correspond to rock-paper-scissors games.


37N25 Dynamical systems in biology
91A22 Evolutionary games
91A60 Probabilistic games; gambling
37A50 Dynamical systems and their relations with probability theory and stochastic processes
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