Control systems of interacting objects modeled as a game against nature under a mean field approach By Carmen Higuera

In this talk we will deal with discrete-time stochastic systems composed of a large
number of N interacting objects. There is a central controller whose decisions,
at each stage, affect the system behavior. Each object evolves randomly among a
finite set of classes, according to a transition law which depends on an unknown
parameter. Such a parameter is possibly non observable and may change from stage
to stage. Due to the lack of information and to the large number of agents, the
control problem under study is rewritten as a game against nature according to the
mean field theory; that is, we introduce a game model associated to the proportions of
the objects in each class, whereas the values of the unknown parameter are now
considered as "actions" selected by an opponent to the controller (the nature).
Then, letting N→∞ (the mean field limit) and considering a discounted optimality
criterion, the objective for the controller is to minimize the maximum cost, where
the maximum is taken over all possible strategies of the nature.