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arXiv · 2012.05562

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

Tsuneya Yoshida·Tomonari Mizoguchi·Yasuhiro Hatsugai
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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.

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Tsuneya Yoshida, Tomonari Mizoguchi, Yasuhiro Hatsugai. 2020-12-10. Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors. https://doi.org/10.1103/physreve.104.025003

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