  Game theory is a very profound study on distributed decision-making behavior
and has been extensively developed by many scholars. However, many existing
works rely on certain strict assumptions such as knowing the opponent's private
behaviors, which might not be practical. In this work, we focused on two Nobel
winning concepts, the Nash equilibrium and the correlated equilibrium.
Specifically, we successfully reached the correlated equilibrium outside the
convex hull of the Nash equilibria with our proposed deep reinforcement
learning algorithm. With the correlated equilibrium probability distribution,
we also propose a mathematical model to inverse the calculation of the
correlated equilibrium probability distribution to estimate the opponent's
payoff vector. With those payoffs, deep reinforcement learning learns why and
how the rational opponent plays, instead of just learning the regions for
corresponding strategies and actions. Through simulations, we showed that our
proposed method can achieve the optimal correlated equilibrium and outside the
convex hull of the Nash equilibrium with limited interaction among players.
