On the distribution of the number of internal equilibria in random evolutionary games with correlated payoff matrix

The analysis of equilibrium points in random games has been of great interest in evolutionary game theory, with important implications for understanding of complexity in a dynamical system, such as its behavioural, cultural or biological diversity. The analysis so far has focused on random games of independent payoff entries. In overcoming this restrictive assumption, here we study equilibrium points in random games with correlated entries. Namely, we analyse the mean value and the distribution of the number of (stable) internal equilibria in multi-player two-strategy evolutionary games where the payoff matrix entries are correlated random variables. Our contributions are as follows. We first obtain a closed formula for the mean number of internal equilibria, characterise its asymptotic behaviour and study the effect of the correlation. We then provide analytical formulas to compute the probability of attaining a certain number of internal equilibria, and derive an approximate formula for the computation of this probability. Last but not least, we reveal some universal estimates that are independent of the distribution of the payoff matrix entries, and provide numerical simulations to support the obtained analytical results.

• Publication year

  2017

• Venue

  arXiv: Analysis of PDEs

• Publication date

  2017-08-04

• Fields of study

  Biology, Mathematics

• Identifiers
  arXiv 1708.01672
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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