NON-COOPERATIVE DIFFERENTIAL GAMES

In a non-cooperative differential game, two or more players can influence the time evolution of a system. Each player chooses a feedback control $u=u(x)$ in order to minimize his own cost functional.

If a Nash equilibrium solution exists, under suitable regularity conditions the value functions satisfy a (highly nonlinear) system of Hamilton-Jacobi equations.

After a general overview, the talk will present a
new analytical approach to the study of these PDEs, based on a homotopy method.

Examples show that this approach is also naturally motivated by some economic models.