  A class of nonzero-sum stochastic dynamic games with imperfect information
structure is investigated. The game involves an arbitrary number of players,
modeled as homogeneous Markov decision processes, aiming to find a sequential
Nash equilibrium. The players are coupled in both dynamics and cost functions
through the empirical distribution of states and actions of players. Two
non-classical information structures are considered: deep state sharing and
no-sharing, where deep state refers to the empirical distribution of the states
of players. In the former, each player observes its local state as well as the
deep state while in the latter each player observes only its local state. For
both finite- and infinite-horizon cost functions, a sequential equilibrium,
called deep Nash equilibrium, is identified, where the dynamics of deep state
resembles a convolutional neural network. In addition, an approximate
sequential equilibrium, called sequential mean-field equilibrium, under
no-sharing information structure is proposed, whose performance converges to
that of the deep Nash equilibrium despite the fact that the strategy is not
necessarily continuous with respect to the deep state. The proposed strategies
are robust to trembling-hand imperfection in both microscopic and macroscopic
levels. Finally, the extension to multiple sub-populations and
arbitrarily-coupled (asymmetric) cost functions are demonstrated.
