Lattice approximations of the first-order mean field type differential games

The theory of first-order mean field type differential games examines the systems infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study approximations value function game using solutions model finite-dimensional games. appears as a continuous-time Markov game, i.e., theoretical problem with and dynamics determined finite state nonlinear chain. Given supersolution (resp. subsolution) Hamilton–Jacobi equation for we construct suboptimal strategy first second) player evaluate approximation accuracy modulus continuity reward distance between original This gives values Furthermore, present way to build approximates given accuracy.