Rock-Paper-Scissors Lattice Model
In this work, we introduce Rock-Paper-Scissors lattice model on Cayley tree of second order generated by Rock-Paper-Scissors game. In this strategic 2-player game, the rule is simple: rock beats scissors, scissors beat paper, and paper beats rock. A payoff matrix A of this game is a skewsymmetric....
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Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
2020
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Subjects: | |
Online Access: | http://irep.iium.edu.my/82349/1/1726-8354-1-PB.pdf http://irep.iium.edu.my/82349/ |
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Institution: | Universiti Islam Antarabangsa Malaysia |
Language: | English |
Summary: | In this work, we introduce Rock-Paper-Scissors lattice model on Cayley tree of second order
generated by Rock-Paper-Scissors game. In this strategic 2-player game, the rule is simple: rock
beats scissors, scissors beat paper, and paper beats rock. A payoff matrix A of this game is a skewsymmetric.
It is known that quadratic stochastic operator generated by this matrix is non-ergodic transformation. The Hamiltonian of Rock-Paper-Scissors Lattice Model is defined by this skewsymmetric payoff matrix A . In this paper, we discuss a connection between three fields of research:
evolutionary games, quadratic stochastic operators, and lattice models of statistical physics. We prove
that a phase diagram of the Rock-Paper-Scissors model consists of translation-invariant and periodic
Gibbs measure with period 3. |
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