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Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games

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Duong, Manh Hong and Han, The Anh (2016) Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games. Journal of Mathematical Biology, 73 (6-7). pp. 1727-1760. doi:10.1007/s00285-016-1010-8 ISSN 0303-6812.

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Official URL: http://dx.doi.org/10.1007/s00285-016-1010-8

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Abstract

In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, fn,dfn,d, and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as √dāˆ’1 as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Game theory, Random polynomials
Journal or Publication Title: Journal of Mathematical Biology
Publisher: Springer
ISSN: 0303-6812
Official Date: December 2016
Dates:
DateEvent
December 2016Published
6 May 2016Valid
23 April 2016Available
7 April 2016Accepted
Volume: 73
Number: 6-7
Page Range: pp. 1727-1760
DOI: 10.1007/s00285-016-1010-8
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 27 July 2016
Date of first compliant Open Access: 23 April 2017

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