On the expected number of equilibria in a multi-player multi-strategy evolutionary game

M.H. Duong, T.A. Han

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Abstract

In this paper, we analyze the mean number $E(n,d)$ of internal equilibria in a general $d$-player $n$-strategy evolutionary game where the agents' payoffs are normally distributed. First, we give a computationally implementable formula for the general case. Next we characterize the asymptotic behavior of $E(2,d)$, estimating its lower and upper bounds as $d$ increases. Then we provide an exact formula for $E(n,2)$. As a consequence, we show that in both cases the probability to see the maximal possible number of equilibria tends to zero when $d$ or $n$ respectively goes to infinity. Finally, for larger $n$ and $d$, numerical results are provided and discussed.
Original languageEnglish
Publishers.n.
Number of pages26
Publication statusPublished - 2014

Publication series

NamearXiv
Volume1408.3850 [math.PR]

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