Extensions for Volume I

The goal of this chapter is to follow-up on some of the examples introduced in Chapter 1, especially those which are not directly covered by the probabilistic theory of stochastic differential mean field games developed so far. Indeed, Chapter 1 included a considerable amount of applications hinting at mathematical models with distinctive features which were not accommodated in the previous chapters. We devote this chapter to presentations, even if only informal, of extensions of the Mean Field Game paradigm to these models. They include extensions to several homogenous populations, infinite horizon optimization, and finite state space models. These mean field game models have a great potential for the quantitative analysis of very important practical applications, and we show how the technology developed in this book can be brought to bear on their solutions.