  We present a new model of incomplete information games without private
information in which the players use a distributionally robust optimization
approach to cope with the payoff uncertainty. With some specific restrictions,
we show that our "Distributionally Robust Game" constitutes a true
generalization of three popular finite games. These are the Complete
Information Games, Bayesian Games and Robust Games. Subsequently, we prove that
the set of equilibria of an arbitrary distributionally robust game with
specified ambiguity set can be computed as the component-wise projection of the
solution set of a multi-linear system of equations and inequalities. For
special cases of such games we show equivalence to complete information finite
games (Nash Games) with the same number of players and same action spaces.
Thus, when our game falls within these special cases one can simply solve the
corresponding Nash Game. Finally, we demonstrate the applicability of our new
model of games and highlight its importance.
