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Persistence probability of a random polynomial arising from evolutionary game theory

Published online by Cambridge University Press:  01 October 2019

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.

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.

Type
Research Papers
Copyright
© Applied Probability Trust 2019 

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