  Coarse correlated equilibria (CCE) are a good alternative to Nash equilibria
(NE), as they arise more naturally as outcomes of learning algorithms and they
may exhibit higher payoffs than NE. CCEs include a device which allows players'
strategies to be correlated without any cooperation, only through information
sent by a mediator. We develop a methodology to concretely compute mean field
CCEs in a linear-quadratic mean field game framework. We compare their
performance to mean field control solutions and mean field NE (usually named
MFG solutions). Our approach is implemented in the mean field version of an
emission abatement game between greenhouse gas emitters. In particular, we
exhibit a simple and tractable class of mean field CCEs which allows to
outperform very significantly the mean field NE payoff and abatement levels,
bridging the gap between the mean field NE and the social optimum obtained by
mean field control.
