(untitled) (Journal of Computational Mathematics, 2021)
The equilibrium strategy for N-person differential games can be obtained from a min-max problem subject to differential constraints. The differential constraints are treated here by the duality and penalty methods. We first formulate the duality theory. This involves the introduction of N+1 Lagrange multipliers: one for each player and one commonly shared by all players. The primal min-max problem thus results in a dual problem, which is a max-min problem with no differential constraints. We develop the penalty theory by penalizing N+1 differential constraints. We give a convergence proof which generalizes a theorem due to B.T. Polyak.