Quadratic stochastic operators and zero-sum game dynamics
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-pa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/1/37341.pdf |
| Summary: | 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. |
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