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

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Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games. / Duong, Manh Hong; Han, The Anh.

In: Journal of Mathematical Biology, Vol. 73, No. 6-7, 12.2016, p. 1727-1760.

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@article{1926fd6a439247b7ae4195b4a657739a,
title = "Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games",
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,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 √d−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.",
keywords = "Random evolutionary games, Internal equilibria, Random polynomials, Multi-player games",
author = "Duong, {Manh Hong} and Han, {The Anh}",
year = "2016",
month = dec,
doi = "10.1007/s00285-016-1010-8",
language = "English",
volume = "73",
pages = "1727--1760",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Nature",
number = "6-7",

}

RIS

TY - JOUR

T1 - Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games

AU - Duong, Manh Hong

AU - Han, The Anh

PY - 2016/12

Y1 - 2016/12

N2 - 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,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 √d−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.

AB - 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,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 √d−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.

KW - Random evolutionary games

KW - Internal equilibria

KW - Random polynomials

KW - Multi-player games

UR - http://wrap.warwick.ac.uk/80462/

U2 - 10.1007/s00285-016-1010-8

DO - 10.1007/s00285-016-1010-8

M3 - Article

VL - 73

SP - 1727

EP - 1760

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6-7

ER -