Coalescence Model of Rock-Paper-Scissors Particles

TL;DR

This paper introduces a novel coalescence model based on rock-paper-scissors interactions, linking kinetic gas theory and coagulation theory, and explores its mathematical properties and discrete behavior.

Contribution

It develops a new extended rock-paper-scissors collision and coalescence model that connects nonlinear integrable systems with physical and biological processes.

Findings

The model links kinetic theory and coagulation theory.

A nonlinear integrable system describes the model's evolution.

Discrete model behavior is analyzed.

Abstract

The rock-paper-scissors game, commonly played in East Asia, gives a simple model to understand physical, biological, psychological and other problems. The interacting rock-paper-scissors particle system is a point of contact between the kinetic theory of gases by Maxwell and Boltzmann ( collision model) and the coagulation theory by Smoluchowski ( coalescence model). A $2s+1$ types extended rock-paper-scissors collision model naturally introduces a nonlinear integrable system. The time evolution of the $2s+1$ types extended rock-paper-scissors coalescence model is obtained from the logarithmic time change of the nonlinear integrable system. We also discuss the behavior of a discrete rock-paper-scissors coalescence model.