Evolutionary games with randomly changing payoff matrices

Journal of the Physical Society of Japan. 2015. Vol. 84. No. 6, Article number 064802. P. 064802-1–064802-7.

Якушкина Т. С., Saakian D., Bratus A., Hu C.

Evolutionary games are used in various elds stretching from economics to biology. Most assume a constant payoff matrix, although some works also consider dynamic payoff matrices. In this article we propose a possibility of switching the system between two regimes with different sets of payoff matrices. Such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A nite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution by applying the Hamilton-Jacobi formalism. Therefore, we present an exactly solvable version of an evolutionary game with annealed noise in the payoff matrix.

Ключевые слова: эволюционное моделирование, Hamilton-Jacobi equation, evolutionary model, evolutionary game theory, эволюционная теория игр, уравнения Гамильтона-Якоби