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

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Title: Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games
Authors: Duong, MH
Han, TA
Item Type: Journal Article
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.
Issue Date: 23-Apr-2016
Date of Acceptance: 25-Mar-2016
URI: http://hdl.handle.net/10044/1/59196
DOI: https://dx.doi.org/10.1007/s00285-016-1010-8
ISSN: 0303-6812
Publisher: Springer
Start Page: 1727
End Page: 1760
Journal / Book Title: Journal of Mathematical Biology
Volume: 73
Issue: 6
Copyright Statement: © 2016 Springer-Verlag Berlin Heidelberg. The final publication is available at https://dx.doi.org/10.1007/s00285-016-1010-8
Keywords: Science & Technology
Life Sciences & Biomedicine
Biology
Mathematical & Computational Biology
Life Sciences & Biomedicine - Other Topics
Random evolutionary games
Internal equilibria
Random polynomials
Multi-player games
STABLE STRATEGIES
BERNSTEIN POLYNOMIALS
REPLICATOR DYNAMICS
NASH EQUILIBRIA
ONE-LOCUS
NUMBER
PATTERNS
SYSTEM
ESSS
FORM
Algorithms
Biological Evolution
Computer Simulation
Cooperative Behavior
Game Theory
Models, Statistical
01 Mathematical Sciences
06 Biological Sciences
Bioinformatics
Notes: mrclass: 91A22 (60G50 92D15) mrnumber: 3556848
Publication Status: Published
Online Publication Date: 2016-04-23
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences