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....
| 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/ http://irep.iium.edu.my/82349/1/1726-8354-1-PB.pdf |
| _version_ | 1848789282265759744 |
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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. |
| first_indexed | 2025-11-14T17:54:14Z |
| format | Article |
| id | iium-82349 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T17:54:14Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |