Vortex generation in the RSP game on the triangular lattice

TL;DR

This paper introduces a new population dynamics model on triangular lattices where players engage in RSP games, leading to steady vortex patterns caused by lattice frustrations, revealing complex spatial structures in strategic interactions.

Contribution

It presents a novel lattice-based RSP model demonstrating vortex formations due to lattice frustrations, highlighting the role of local conflicts in population dynamics.

Findings

Vortex and sink patterns emerge on the triangular lattice.

Stationary vortices are caused by frustrations in player choices.

Triangular lattice frustrations lead to complex steady-state patterns.

Abstract

A new model of population dynamics on lattices is proposed. The model consists of players on lattice points, each of which plays the RSP game with neighboring players. Each player copies the next hand from the hand of the neighbouring player with the maximum point. The model exhibits a steady pattern with pairs of vortices and sinks on the triangular lattice. It is shown that the stationary vortex is due to the frustrations on the triangular lattice. A frustration is the three-sided situation where each of the three players around a triangle chooses the rock, the scissors and the paper, respectively.