Weak Convergence in Many Player Games

Abstract

In this chapter, we will discuss the weak convergence methods for n-person games. The entire problem will be set in a relaxed control framework. The advantage is that the problem becomes linear in control variables. The main advantage of occupation measure setting is that the differential game problem reduces to a static game on the set of occupation measures, the dynamics of the game being captured in these measures. In the proofs, we will use the weak convergence theory. We will only explain the case of averege payoffs. Discounted and other payoffs structure can be dealt in a similar fasion.