On the Expected Number of Equilibria in a Multi-player Multi-strategy Evolutionary Game

Manh Hong Duong () and The Anh Han ()
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Manh Hong Duong: University of Warwick
The Anh Han: Teesside University

Dynamic Games and Applications, 2016, vol. 6, issue 3, No 4, 324-346

Abstract: Abstract In this paper, we analyze the mean number $$E(n,d)$$ E ( n , d ) of internal equilibria in a general $$d$$ d -player $$n$$ 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 $$E(2,d)$$ E ( 2 , d ) , estimating its lower and upper bounds as $$d$$ d increases. Then we provide a closed formula for $$E(n,2)$$ E ( n , 2 ) . Two important consequences are obtained from this analysis. On the one hand, we show that in both cases, the probability of seeing the maximal possible number of equilibria tends to zero when $$d$$ d or $$n$$ n , respectively, goes to infinity. On the other hand, we demonstrate that the expected number of stable equilibria is bounded within a certain interval. Finally, for larger $$n$$ n and $$d$$ d , numerical results are provided and discussed.

Keywords: Evolutionary game; Multi-player games; Multiple strategies; Random polynomials; Number of equilibria; Random games (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13235-015-0148-0

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