Vortex generation in the RSP game on the triangular lattice

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