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Persistence probability of a random polynomial arising from evolutionary game theory

Part of: Geometric function theory Game theory Polynomials, rational functions

Published online by Cambridge University Press:  01 October 2019

Van Hao Can ,
Manh Hong Duong  and
Viet Viet Hung Pham
Van Hao Can*
Affiliation:
Vietnam Academy of Science and Technology, and Kyoto University
Manh Hong Duong*
Affiliation:
University of Birmingham
Viet Viet Hung Pham*
Affiliation:
Vietnam Academy of Science and Technology
*
*Postal address: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Street, 10307 Hanoi, Vietnam.
**Postal address: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK.
*Postal address: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Street, 10307 Hanoi, Vietnam.
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Abstract

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.

Keywords

Random polynomialevolutionary game theorypersistence probabilityequilibrium pointGaussian process

MSC classification

Primary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
Secondary: 26C10: Polynomials 91A22: Evolutionary games
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 870 - 890
Copyright
© Applied Probability Trust 2019 

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