Coalitional fair allocations in smooth mixed markets with an atomless sector

An appropriate model for an oligopolistic economy is a mixed market consisting of some large traders and an ocean of small traders. For such a market, an allocation is λ-coalitionally fair (λ-c-fair) if it is Pareto optimal and no coalition of traders can benifit by exchanging its net trade with that of another coalition which is disjoint and has the same measure λ. It is shown that all λ-c-fair allocations have Pareto prices under which the value of the net trade of every small trader is the same. In some classes of markets, the set of λ-c-fair allocations coincides with the set of competitive allocations. These results can be contrasted with the analysis of the cores for mixed markets (see either Gabszewicz and Shitovitz, 1992, for a survey or Shitovitz, 1973, for an elementary introduction to such models).