THE SOLUTION OF EVOLUTIONARY GAMES USING THE THEORY OF HAMILTON-JACOBI EQUATIONS

A dynamical model of a non-antagonistic evolutionary game for two coal itions is considered. The model features an infinite time span and dis counted payoff functionals. A solution is presented using differential game theory. The solution is based on the construction of a value fun ction for auxiliary antagonistic differential games and uses an approx imate grid scheme from the theory of generalized solutions of the Hami lton-Jacobi equations. Together with the value functions the optimal g uaranteeing procedures for control on the grid are computed and the Na sh dynamic equilibrium is constructed. The behaviour of trajectories g enerated by the guaranteeing controls is investigated. Examples are gi ven.