Rock-Paper-Scissors Lattice Model

• Main Authors: Ganikhodjaev, Nasir, Pah, Chin Hee
• Format: Article
• Language: English
• Published: 2020
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/82349/1/1726-8354-1-PB.pdf; http://irep.iium.edu.my/82349/
• Institution: Universiti Islam Antarabangsa Malaysia

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.