Non-Hermitian topology in rock-paper-scissors games

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.

arXiv comment6+6 pages, 4+5 figures

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• Supporting punishment via taxation in a structured population
• Fate of exceptional points under interactions: Reduction of topological classifications
• Competition of alliances in a cyclically dominant eight-species population
• Emerging solutions from the battle of defensive alliances
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Discriminant indicators with generalized inversion symmetry
• When faster rotation is harmful: the competition of alliances with inner blocking mechanism
• Competition among alliances of different sizes
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• Hermitian and non-Hermitian topology in active matter
• Topological phases in discrete stochastic systems
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• Exceptional mode topological surface laser
• Topological phase transition in anti-symmetric Lotka-Volterra doublet chain
• Emergence of first-order and second-order phase transitions in a cyclic ecosystem exposed to environmental impact
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields