Non-Hermitian topology in rock-paper-scissors games

TL;DR

This paper explores non-Hermitian topological phenomena, such as exceptional points and skin effects, within rock-paper-scissors game models, revealing novel dynamical behaviors and opening interdisciplinary research avenues.

Contribution

It introduces a new interdisciplinary platform linking non-Hermitian topology with evolutionary game theory, demonstrating topological effects in RPS cycles.

Findings

Emergence of exceptional points in RPS payoff matrices

Observation of skin effects and directed population propagation

Population density enhancement at the chain's edge

Abstract

Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock-paper-scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory.