An explicit bound on

We consider parameterized collections of games without side payments and determine a bound on epsilon so that all sufficiently large games in the collection have non-empty epsilon-cores. The required size of epsilon depends on: (a) the number of approximate player types and the accuracy of this approximation; (b) the size of approximately effective small groups; (c) the size of the bound on maximal per-capita payoffs achievable in coalitions; and (d) a measure on the extent to which the payoff sets of the games are bounded away from being ``flat.'' Our result makes explicit the relationship between the required size of epsilon for non-emptiness of the epsilon-core, the parameters describing the collection.