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

Van Hao Can; Manh Hong Duong; Viet Hung Pham

doi:10.4310/CMS.2022.v20.n6.a7

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

Van Hao Can, Manh Hong Duong, Viet Hung Pham

Mathematics

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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.

Original language	English
Pages (from-to)	1613-1636
Number of pages	24
Journal	Communications in Mathematical Sciences
Volume	20
Issue number	6
DOIs	https://doi.org/10.4310/CMS.2022.v20.n6.a7
Publication status	Published - 14 Sept 2022

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10.4310/CMS.2022.v20.n6.a7Licence: None: All rights reserved

DuongM2022expected
This is the accepted manuscript for a forthcoming publication in Communications in Mathematical Sciences. The final version of record will be available at: http://www.intlpress.com/CMS/
Accepted author manuscript, 430 KBLicence: None: All rights reserved

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title = "On the expected number of real roots of random polynomials arising from evolutionary game 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.",

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AU - Duong, Manh Hong

AU - Pham, Viet Hung

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N2 - 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.

AB - 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.

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DO - 10.4310/CMS.2022.v20.n6.a7

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JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

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

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