  We consider a finite horizon repeated game with $N$ selfish players who
observe their types privately and take actions, which are publicly observed.
Their actions and types jointly determine their instantaneous rewards. In each
period, players jointly observe actions of each other with delay 1, and private
observations of the state of the system, and get an instantaneous reward which
is a function of the state and everyone's actions. The players' types are
static and are potentially correlated among players.
  An appropriate notion of equilibrium for such games is Perfect Bayesian
Equilibrium (PBE) which consists of a strategy and a belief profile of the
players which is coupled across time and as a result, the complexity of finding
such equilibria grows double-exponentially in time. We present a sequential
decomposition methodology to compute \emph{structured perfect Bayesian
equilibria} (SPBE) of this game, introduced in~\cite{VaAn15arxiv}, where
equilibrium policy of a player is a function of a common belief and a private
state. This methodology computes SPBE in linear time. In general, the SPBE of
the game problem exhibit \textit{signaling} behavior, i.e. players' actions
reveal part of their private information that is payoff relevant to other
players.
