Constructive -Nash Equilibria for Nonzero-Sum Differential Games


During this paper, a category of infinite-horizon, nonzero-add differential games and their Nash equilibria are studied and also the notion of $epsilon_alpha $-Nash equilibrium strategies is introduced. Dynamic strategies satisfying partial differential inequalities in preference to the Hamilton–Jacobi–Isaacs partial differential equations related to the differential games are constructed. These methods constitute (native) $epsilon_alpha $-Nash equilibrium methods for the differential game. The proposed ways are illustrated on a differential game for that the Nash equilibrium methods are known and on a Lotka–Volterra model, with two competing species. Simulations indicate that each dynamic methods yield higher performance than the methods ensuing from the answer of the linear-quadratic approximation of the problem.

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