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Jamilov, Uygun; Ladra, Manuel

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

Qual. Theory Dyn. Syst. 15, No. 1, 257-271 (2016).
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.

Cited in 19 Documents

MSC:

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

Keywords:

ergodic hypothesis; Volterra quadratic stochastic operator; tournament; zero-sum game; rock-paper-scissors game
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\textit{U. Jamilov} and \textit{M. Ladra}, Qual. Theory Dyn. Syst. 15, No. 1, 257--271 (2016; Zbl 1344.37093)
Full Text: DOI

References:

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