Asymptotic value of games with a continuum of players

We investigate the asymptotic value for a class of non-atomic games, which includes all those arising from markets with a continuum of traders. The main result is the following: the asymptotic value, if it exists, is the center of symmetry of the core. This implies that the value is a member of the core, and it gives a necessary condition for its existence. The sufficiency of this condition for the existence of the value is also studied.