Mean-field game theory and economic applications: second topic: Discount rates and sustainable development.

Summary Introduced by J. -M. Lasry and P.-L. Lions, mean-field game theory simplifies interactions between economic agents using an approach inspired by physical theories. Economic applications are presented concerning the labor market, asset management, population distribution problems, and growth theory. The models presented use mean-field game theory in various forms, sometimes static, often dynamic, with discrete or continuous state space and in a deterministic or stochastic environment. Various notions of stability are discussed, including the notion of educative stability, which has inspired numerical methods of resolution. Indeed, we present numerical methods that allow to obtain solutions to both stationary and dynamic problems, while abstracting from the forward/backward structure, which is a priori problematic from a numerical point of view. In the margin of mean-field game theory, the problem of appropriate discount rates to deal with sustainable development problems is addressed. We discuss the notion of ecological rate introduced by R. Guesnerie and provide new non-asymptotic properties, notably continuity.