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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
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Official URL: http://dx.doi.org/10.1007/s00285-016-1010-8
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 √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.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of 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: |
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| Date of first compliant deposit: | 27 July 2016 | ||||||||||
| 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 |
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