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The solution of evolutionary games using the theory of Hamilton-Jacobi equations. (English. Russian original) Zbl 0885.90135

J. Appl. Math. Mech. 59, No. 6, 921-933 (1995); translation from Prikl. Mat. Mekh. 59, No. 6, 965-979 (1995).
Summary: A dynamical model of a non-antagonistic evolutionary game for two coalitions is considered. The model features an infinite time span and discounted payoff functionals. A solution is presented using differential game theory. The solution is based on the construction of a value function for auxiliary antagonistic differential games and uses an approximate grid scheme from the theory of generated solutions of the Hamilton-Jacobi equations. Together with the value functions the optimal guaranteeing procedures for control on the grid are computed and the Nash dynamic equilibrium is constructed. The behaviour of trajectories generated by the guaranteeing controls is investigated. Examples are given.

MSC:

91A23 Differential games (aspects of game theory)
70H20 Hamilton-Jacobi equations in mechanics
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