  Inspired by the concepts of deep learning in artificial intelligence and
fairness in behavioural economics, we introduce deep teams in this paper. In
such systems, agents are partitioned into a few sub-populations so that the
dynamics and cost of agents in each sub-population is invariant to the indexing
of agents. The goal of agents is to minimize a common cost function in such a
manner that the agents in each sub-population are not discriminated or
privileged by the way they are indexed. Two non-classical information
structures are studied. In the first one, each agent observes its local state
as well as the empirical distribution of the states of agents in each
sub-population, called deep state, whereas in the second one, the deep states
of a subset (possibly all) of sub-populations are not observed. Novel dynamic
programs are developed to identify globally optimal and sub-optimal solutions
for the first and second information structures, respectively. The
computational complexity of finding the optimal solution in both space and time
is polynomial (rather than exponential) with respect to the number of agents in
each sub-population and is linear (rather than exponential) with respect to the
control horizon. This complexity is further reduced in time by introducing a
forward equation, that we call deep Chapman-Kolmogorov equation, described by
multiple convolutional layers of Binomial probability distributions. Two
different prices are defined for computation and communication, and it is shown
that under mild assumptions they converge to zero as the quantization level and
the number of agents tend to infinity. In addition, the main results are
extended to the infinite-horizon discounted model and arbitrarily asymmetric
cost function. Finally, a service-management example with 200 users is
presented.
