Chiral edge modes in evolutionary game theory: A kagome network of rock-paper-scissors cycles.

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 nontrivial 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 the cyclic motion of a single rock-paper-scissors cycle, which is analogous to the cyclotron motion of fermions. Furthermore, we point out that a linearized LV equation is mathematically equivalent to the Schrödinger equation describing quantum systems. This equivalence allows us to clarify the topological origin of the chiral edge mode in the K-RPS; a nonzero 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.