This week

Coarse correlated equilibria are generalizations of Nash equilibria which have first been introduced in Moulin et Vial (1978). They include a correlation device which can be interpreted as a mediator recommending strategies to the players, which makes it particularly relevant in a context of market failure. After establishing an existence and approximation results result in a fairly general setting, we develop a methodology to compute mean-field coarse correlated equilibria (CCEs) in a linear-quadratic framework. We identify cases in which CCEs outperform Nash equilibria in terms of both social utility and control levels. Finally, we apply such a methodology to a CO2 abatement game between countries (a slightly modified version of Barrett (1994)). We show that in that model CCEs allow to reach higher abatement levels than the NE, with higher global utility. The talk is based on joint works with F. Cannerozzi (Milan University), F. Cartellier (ENSAE) and M. Fischer (Padua University).

Consider the following mean-field equation on R^d:
d X_t = V(X_t, mu_t) dt + d B_t,
where mu_t is the law of X_t, the drift V(x, mu) is smooth and confining, and (B_t) is a standard Brownian motion.
This McKean-Vlasov equation may admit multiple invariant probability measures.
I will discuss the (local) stability of one of these equilibria.
Using Lions derivatives, a stability criterion is derived, analogous to the Jacobian stability criterion for ODEs.
Under this spectral condition, the equilibrium is shown to be attractive for the Wasserstein metric W1.
In addition, I will discuss a metastable behavior of the
associated particle system, around a stable equilibrium of the mean-field equation.