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Rock-Paper-Scissors Lattice Model

Ganikhodjaev, Nasir and Pah, Chin Hee (2020) Rock-Paper-Scissors Lattice Model. Malaysian Journal of Fundamental and Applied Sciences. ISSN 1823-8343

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Abstract

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.

Item Type: Article (Journal)
Additional Information: 4430/82349
Uncontrolled Keywords: Rock-Paper-Scissors Lattice Model
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: DR. CHIN HEE PAH
Date Deposited: 24 Aug 2020 15:23
Last Modified: 24 Aug 2020 15:23
URI: http://irep.iium.edu.my/id/eprint/82349

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