It was suggested in [2] that an appropriate model for an oligopolistic economy is one in which the set of traders consists of some large traders and a continuum of small traders. The cores of such market models are analyzed here. Some of the results are as follows: A duopolistic market in which the duopolists are of the same type is "perfectly competitive," i.e., its core coincides with the set of competitive allocations. At any allocation in the core of any oligopolistic markets, the value of the bundle received by a small trader does not exceed the value of his initial bundle; that is, small traders can never "gain money." Conditions are given under which small traders will not "lose money" either. In addition to the case of duopoly, other conditions are given under which an oligopolistic market will be perfectly competitive.