Work

Random evolutionary games and random polynomials

Year: 2025

Type: article

Abstract: In this paper, we discover that the class of random polynomials arising from the equilibrium analysis of random asymmetric evolutionary games is exactly the Kostlan–Shub–Smale system of random polynomials, revealing an intriguing connection between evolutionary game theory and the theory of random polynomials. Through this connection, we analytically characterize the statistics of the number of internal equilibria of random asymmetric evolutionary games, namely its mean value, probability distribution, central limit theorem and universality phenomena. Biologically, these quantities enable the prediction of the levels of social and biological diversity as well as the overall complexity in a dynamical system. By comparing symmetric and asymmetric random games, we establish that symmetry in group interactions increases the expected number of internal equilibria. Our analysis establishes new theoretical understanding of asymmetric evolutionary games and highlights the significance of symmetry and asymmetry in group interactions.

Source: Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

DOI: 10.1098/rspa.2024.0911

Authors: Manh Hong Duong, The Anh Han

Institutions: University of Birmingham, Teesside University

Language: English

Topic: Evolutionary Game Theory and Cooperation

Subfield: Sociology and Political Science

Field: Social Sciences

Domain: Social Sciences

Open Access status: hybrid

Funders: Future of Life Institute, Royal Society, Engineering and Physical Sciences Research Council

Awards: Evolutionary Game Theory Under Uncertainty, Evolutionary Game Theory Under Uncertainty, G4543150891, G5247048433