  We study the core of normal form games with a continuum of players and
without side payments. We consider the weak-core concept, which is an
approximation of the core, introduced by Weber, Shapley and Shubik. For payoffs
depending on the players' strategy profile, we prove that the weak-core is
nonempty. The existence result establishes a weak-core element as a limit of
elements in weak-cores of appropriate finite games. We establish by examples
that our regularity hypotheses are relevant in the continuum case and the
weak-core can be strictly larger than the Aumann's $\alpha$-core. For games
where payoffs depend on the distribution of players' strategy profile, we prove
that analogous regularity conditions ensuring the existence of pure strategy
Nash equilibria are irrelevant for the non-vacuity of the weak-core.
