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: Ganikhodjaev, Nasir, Pah, Chin Hee
Format: Article
Language:English
Published: 2020
Subjects:
Online Access:http://irep.iium.edu.my/82349/
http://irep.iium.edu.my/82349/1/1726-8354-1-PB.pdf
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author Ganikhodjaev, Nasir
Pah, Chin Hee
author_facet Ganikhodjaev, Nasir
Pah, Chin Hee
author_sort Ganikhodjaev, Nasir
building IIUM Repository
collection Online Access
description 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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institution International Islamic University Malaysia
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spelling iium-823492020-11-24T08:34:04Z http://irep.iium.edu.my/82349/ Rock-Paper-Scissors Lattice Model Ganikhodjaev, Nasir Pah, Chin Hee QA Mathematics 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. 2020-08-21 Article PeerReviewed application/pdf en http://irep.iium.edu.my/82349/1/1726-8354-1-PB.pdf Ganikhodjaev, Nasir and Pah, Chin Hee (2020) Rock-Paper-Scissors Lattice Model. Malaysian Journal of Fundamental and Applied Sciences. ISSN 1823-8343
spellingShingle QA Mathematics
Ganikhodjaev, Nasir
Pah, Chin Hee
Rock-Paper-Scissors Lattice Model
title Rock-Paper-Scissors Lattice Model
title_full Rock-Paper-Scissors Lattice Model
title_fullStr Rock-Paper-Scissors Lattice Model
title_full_unstemmed Rock-Paper-Scissors Lattice Model
title_short Rock-Paper-Scissors Lattice Model
title_sort rock-paper-scissors lattice model
topic QA Mathematics
url http://irep.iium.edu.my/82349/
http://irep.iium.edu.my/82349/1/1726-8354-1-PB.pdf