The Equitable Bargaining Set

We define the equitable bargaining set for exchange economies. Our definition differs from that in Mas-Colell (1989) because it requires that objections and counterobjections must satisfy some equitability conditions. We show that the equitable bargaining set coincides with that of Mas-Colell when the underlying economy is atomless, but not in general. Then we provide two sets of conditions for economies with market imperfections that apply to finite economies and to mixed market economies. In the first case our conditions imply that the equitable bargaining set is a subset of the core, and so it converges to the set of competitive allocations if the economy is replicated. In the second case, we show that all allocations in the equitable bargaining set are competitive, extending the Walras-bargaining equivalence of Mas-Colell (1989) to the framework of mixed markets. All the conditions we use follow from wellestablished assumptions from the literature in finite and mixed market economies.