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

TL;DR

This paper provides finite estimates and asymptotic formulas for the expected number of real roots of certain random polynomials from evolutionary game theory, including internal equilibria in multi-player two-strategy games.

Contribution

It introduces new asymptotic formulas for real roots of polynomials from evolutionary game theory, linking game dynamics with random polynomial analysis.

Findings

Finite estimates for real roots of specific random polynomials

Asymptotic formulas for expected internal equilibria

Bridging evolutionary game theory with random polynomial theory

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.