## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**Title:** Nash Equilibrium Solutions for Noncooperative Nonzero-sum Differential Games

**Speaker:** Fabio Priuli

**Speaker Info:** Institutt for matematiske fag Norwegian University of Science and Technology, Trondheim, Norway

**Brief Description:**

**Special Note**:

**Abstract:**

In this seminar, I will give an introduction to the study of Nash equilibrium solutions for non-cooperative non-zero sum differential
games. This problem is related to the existence of solutions for a suitable system of Hamilton-Jacobi equations.
Being a non-zero sum game, the system cannot be reduced to a single HJ equation and therefore standard tools of viscosity solutions theory cannot be
applied.
Nevertheless, under suitable assumptions on the cost functions of each player, existence and uniqueness can still be recovered, both in the case of
finite horizon and infinite horizon games.
In fact, the two problems need slightly different approaches. For finite horizon games, as shown by Bressan and Shen, the Hamilton Jacobi equations
are related to a system of conservation laws and well posedness turns out to be strictly related to hyperbolicity.
On the other hand, as proved in a joint work with Bressan, Nash equilibria for infinite horizon games lead to a system of ODEs which has admissible
solutions under weaker assumptions.

**Date:** Thursday, November 29, 2007

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Laura Spinolo

**Contact email:** spinolo@math.northwestern.edu

**Contact Phone:** 847-467-1823

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