[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.]

The authors introduce and analyze 'multistage situations, ' which generalize 'multistage games' (which, in turn, generalize 'repeated games'). One reason for this generalization is to avoid the perhaps unrealistic constraints--inherent to noncooperative games--that the set of strategy tuples must be a Cartesian product of the strategy sets of the players. Another reason is that, in most economic and social activities (e.g., in sequential bargaining without a rigid protocol), the 'rules of the game' are rather amorphous; the procedures are rarely pinned down. Such social environments can, however, be represented as multistage situations and be effectively analyzed through the theory of social situations.