We develop a new model of a continuum economy with coalitions consisting of only finite numbers of agents. The core, called the f-core, is the set of allocations that are stable against improvement by finite coalitions and feasible by trade within finite coalitions. Even with widespread externalities-preferences depend on own consumptions and also on the entire allocation up to the null set-we obtain the result that the f-core coincides with the Walrasian allocations. Without widespread externalities, the f-core, the Aumann core, and the Walrasian allocations all coincide; however, with widespread externalities there is no obvious natural definition of the Aumann core.
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