Communications in Mathematical Sciences

Volume 20 (2022)

Number 6

On the expected number of real roots of random polynomials arising from evolutionary game theory

Pages: 1613 – 1636

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n6.a7

Authors

Van Hao Can (Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam; and Department of Statistics and Data Science, National University of Singapore, Singapore)

Manh Hong Duong (School of Mathematics, University of Birmingham, United Kingdom)

Viet Hung Pham (Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam)

Abstract

In this paper, we obtain finite estimates and asymptotic formulas for the expected number of real roots of two classes of random polynomials arising from evolutionary game theory. As a consequence of our analysis, we achieve an asymptotic formula for the expected number of internal equilibria in multi-player two-strategy random evolutionary games. Our results contribute both to evolutionary game theory and random polynomial theory.

Keywords

evolutionary game theory, random polynomials, multi-player two-strategy games, equilibrium points

2010 Mathematics Subject Classification

60F99, 91A22, 92D25

Received 3 March 2021

Received revised 17 January 2022

Accepted 17 January 2022

Published 14 September 2022