Constructive $\epsilon$-Nash Equilibria for Nonzero-Sum Differential Games.

In this paper, a class of infinite-horizon, nonzero-sum differential games and their Nash equilibria are studied and the notion of \epsilon\alpha -Nash equilibrium strategies is introduced. Dynamic strategies satisfying partial differential inequalities in place of the Hamilton–Jacobi–Isaacs partial differential equations associated with the differential games are constructed. These strategies constitute (local) \epsilon\alpha -Nash equilibrium strategies for the differential game. The proposed methods are illustrated on a differential game for which the Nash equilibrium strategies are known and on a Lotka–Volterra model, with two competing species. Simulations indicate that both dynamic strategies yield better performance than the strategies resulting from the solution of the linear-quadratic approximation of the problem. [ABSTRACT FROM AUTHOR]