Persistence probability of a random polynomial arising from evolutionary game theory

TL;DR

This paper derives an asymptotic formula for the probability that a specific random polynomial from evolutionary game theory has no internal equilibria, using Gaussian process approximations.

Contribution

It introduces a novel asymptotic analysis of persistence probabilities for polynomials from evolutionary game models, connecting polynomial behavior with Gaussian processes.

Findings

Derived an asymptotic formula for persistence probability

Linked polynomial properties to Gaussian process approximations

Provided insights into the stability of multi-player evolutionary games

Abstract

In this paper, we obtain an asymptotic formula for the persistence probability in the positive real line of a random polynomial arising from evolutionary game theory. It corresponds to the probability that a multi-player two-strategy random evolutionary game has no internal equilibria. The key ingredient is to approximate the sequence of random polynomials indexed by their degrees by an appropriate centered stationary Gaussian process.