Learning by Examples: What Is a Mean Field Game?

Abstract

The goal of this first chapter is to introduce a diverse collection of examples of games whose descriptions help us introduce the notation and terminology as well as some preliminary results at the core of the theory of mean field games. This compendium of models illustrates the great variety of applications which can potentially be studied rigorously by means of this concept. These introductory examples are chosen for their simplicity, and for pedagogical reasons, we take shortcuts and ignore some of their key features. As a consequence, they will need to be revisited before we can subject them to the treatment provided by the theoretical results developed later on in the book. Moreover, some of the examples may not fit well with the typical models analyzed mathematically in this text as the latter are most often in continuous time, and of the stochastic differential variety. For this reason, we believe that the best way to think about this litany of models is to remember a quote by Box and Draper “All models are wrong, but some are useful”.