  We consider a large population dynamic game in discrete time where players
are characterized by time-evolving types. It is a natural assumption that the
players' actions cannot anticipate future values of their types. Such games go
under the name of dynamic Cournot-Nash equilibria, and were first studied by
Acciaio et al., as a time/information dependent version of the games devised by
Blanchet and Carlier for the static situation, under an extra assumption that
the game is of potential type. The latter means that the game can be reduced to
the resolution of an auxiliary variational problem.
  In the present work we study dynamic Cournot-Nash equilibria in their natural
generality, namely going beyond the potential case. As a first result, we
derive existence and uniqueness of equilibria under suitable assumptions.
Second, we study the convergence of the natural fixed-point iterations scheme
in the quadratic case. Finally we illustrate the previously mentioned results
in a toy model of optimal liquidation with price impact, which is a game of
non-potential kind.
