Work

Bifurcation analysis of an asymmetric three-player three-strategy game with logit dynamics and reverse-cyclic mutations

Year: 2025

Type: article

Abstract: Rock-Paper-Scissors (RPS) games have been widely studied, while research on asymmetric multiplayer cases has remained relatively limited. In this paper, we constructed a three-player asymmetric RPS model by introducing a novel payoff matrix, which then serves as the basis for developing a reverse-cyclic mutation logit system. Analysis of the interior equilibrium showed that both mutation rate and selection intensity can destabilize the equilibrium and generate oscillatory dynamics through Hopf bifurcations. When the first Lyapunov coefficient vanished, the second Lyapunov coefficient was derived to classify the bifurcation type, enabling us to distinguish supercritical and subcritical cases. Numerical simulations confirmed the theoretical predictions. These results revealed stability conditions and bifurcation mechanisms in asymmetric multiplayer interactions and demonstrated how higher-order Lyapunov coefficients enhance the analysis of complex dynamics.

Source: AIMS Mathematics

DOI: 10.3934/math.2025988

Authors: Jie Liu, Wenjun Hu

Institutions: North University of China, Luliang University

Language: English

Topic: Evolutionary Game Theory and Cooperation

Subfield: Sociology and Political Science

Field: Social Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: National Natural Science Foundation of China