An Explicit Bound on epsilon for Non-Emptiness of the epsilon-Core of an Arbitrary Game with Side Payments.

We introduce the concept of a paramaterized collection of games with side payments and determine a bound on epsilon so that all sufficiently large games in such a collection have non-emplty epsilon-cores. A parametrized collection of games is described by (a) the number of approximate player types and the accuracy of this approximation, (b) the size of approximately effective small groups, and (c) the size of the bound on maximal per capita payoffs achievable in coalitions.