TY - BOOK

T1 - On the expected number of equilibria in a multi-player multi-strategy evolutionary game

AU - Duong, M.H.

AU - Han, T.A.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

M3 - Report

T3 - arXiv

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

PB - s.n.

ER -