Open and Closed Loop Nash Equilibria in Games with a Continuum of Players

In this paper, the problem of relations between closed loop and open loop Nash equilibria is examined in the environment of discrete time dynamic games with a continuum of players and a compound structure encompassing both private and global state variables. An equivalence theorem between these classes of equilibria is proven, important implications for the calculation of these equilibria are derived and the results are presented on models of a common ecosystem exploited by a continuum of players. An example of an analogous game with finitely many players is also presented for comparison.