WP5 - Differential Games

• State of the art

The theory of differential games began in the 50s with the work of R. Isaacs motivated by military problems. Since then this field grew enormously, on the mathematical side as well as in the number and diversity of applications, from engineering to economics, social sciences, biology etc. In general the theory deals with dynamical systems controlled by several agents with different goals. A typical example is the worst case analysis of a control system affected by an unknown disturbance, where the disturbance is modeled as an opposing player. The Hamilton-Jacobi-Isaacs (HJI) equations and systems are a fundamental tool in the subject. For two-person, zero-sum differential games the HJI equation is well understood in the framework of viscosity solutions, and efficient algorithms for the numerical approximation of equilibrium strategies are a current topic of research. The theory for non-zero-sum many-person games and the associated systems of Hamilton-Jacobi equations are a largely open field. The limit of feedback Nash equilibria as the number of players go to infinity is the subject of the new-born and promising theory of Mean Field Games.

• Objectives

One of the goals of the WP is developing the theory of Mean Field Games beyond the model (periodic) problems studied by Lasry and Lions. We also aim at understanding the convergence of several approximation procedures for zero-sum games, from time-discretization to dynamic programming numerical schemes, including the approximate synthesis of a feedback via the value function and its robustness.

• Fellows projects

• Planned person-months: 108