Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors

TL;DR

This paper demonstrates that a kagome network of rock-paper-scissors in evolutionary game theory can host topologically protected chiral edge modes, revealing a novel intersection of topology and population dynamics.

Contribution

It introduces the concept of topological edge modes in a non-natural system, linking the Lotka-Volterra equations to topological physics through the Chern number.

Findings

Chiral edge modes are numerically demonstrated in the K-RPS system.

The LV equation is shown to be equivalent to the Schrödinger equation.

A non-zero Chern number induces topologically protected edge states.

Abstract

We theoretically demonstrate the realization of a chiral edge mode in a system beyond natural science. Specifically, we elucidate that a kagome network of rock-paper-scissors (K-RPS) hosts a chiral edge mode of the population density which is protected by the non-trivial topology in the bulk. The emergence of the chiral edge mode is demonstrated by numerically solving the Lotka-Volterra (LV) equation. This numerical result can be intuitively understood in terms of cyclic motion of a single RPS cycle which is analogues to the cyclotron motion of fermions. Furthermore, we point out that a linearized LV equation is mathematically equivalent to the Schr\"odinger equation describing quantum systems. This equivalence allows us to clarify the topological origin of the chiral edge mode in the K-RPS; a non-zero Chern number of the payoff matrix induces the chiral edge mode of the population density, which exemplifies the bulk-edge correspondence in two-dimensional systems described by evolutionary game theory.