Noncooperative Differential Games

The theory of noncooperative games provides a mathematical tool to describe interactions between two or more agents with different goals. It has found widespread applications in economics and management science.

The first part of this talk will review the basic definitions of Nash and Stackelberg solutions, based on the concept of "best reply".   

For games in continuous time,  equilibrium solutions can be found by studying a particular system of Partial Differential Equations. Within the talk, I shall explain how to derive these PDEs, and what are the main difficulties toward their solution.
 
Some current research directions will be discussed, together with applications. As an example, I shall present a model of optimal debt management, viewed as a noncooperative game between a borrower and a pool of lenders.