Convexity and Hamiltonian Equations in Differential Games
Abstract
We study a zero sum differential game under strong assumptions of convexity - the cost is one convex for one player, and concave for the other. An explicit necessary and sufficient condition for a saddle point of the game is given in terms of convex analysis subgradients of the conjugate of the cost function. A generalized Hamiltonian equation is shown to describe saddle trajectories of the game.