Achille Basile

Finitely Additive Nonatomic Coalition Production Economies: Core-Walras Equivalence

The concept of coalition production economy is naturally extended to the finitely additive setting. Let (V, F, v) be the (nonatomic finitely additive probability) space of economic agents. It is proved that a production set correspondence admits plenty of finitely additive selections provided it is finitely additive, closed valued and v-absolutely continuous. As a consequence, a Core-Walras equivalence theorem is established. Copyright 1993 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

On the edgeworth's conjecture in finitely additive economies with restricted coalitions

Abstract With reference to a model of finitely additive economies, we characterize in terms of decentralizing prices several notions of core allocations resulting from different possible restrictions imposed to the set of blocking coalitions. Reciprocal relations among cores are also studied. The model we deal with is based on the coalitional one due to K. Vind. Our investigation analyzes the perfectly competitive case and extends to the oligopolistic case.

Coalitional economies with public projects

We prove that the welfare theorems hold in the framework of coalitional exchange economies with public projects, both in case of pure exchange and in the presence of production. The space of agents is assumed to be non-atomic (single traders are negligible) and infinitely many commodities are allowed to be present on the market.

Sequential compactness for sets of Sugeno fuzzy measures

Abstract Pointwise sequential compactness for families of Sugeno measures is studied and a sufficient condition is proved for the equivalence between equiabsolute continuity, uniform order continuity and sequential compactness. A group-valued measure interpretation for λ-additive fuzzy measures is also showed.

On the Liapunov-Richter theorem in the finitely additive setting

Abstract The range of a finitely additive closed-valued nonatomic correspondence is convex if the domain is a σ-algebra.

Oligopoly and cost sharing in economies with public goods

We study economies that involve both small and large traders as well as the choice of a public project. Within this framework, we establish two sufficient conditions under which the set of competitive allocations coincides with the core. Our first core equivalence result holds under the assumption that there is a countably infinite set of large traders similar to each other. The second result, independent of the number of large traders, requires the existence of a coalition of small traders with the same characteristics of the large traders. Finally, we show how the generalized Aubin approach to cooperation may dispense with both conditions.

A new view on Arrovian dictatorship in a fuzzy setting

Abstract In this note, we obtain new Arrovian results in the setting where the preferences of individuals are fuzzy and no properties of asymmetry are required. Dealing with a society made of possibly infinitely many individuals, we obtain the existence of a unique ultrafilter of decisive coalitions for every Fuzzy Social Welfare Function that obeys to Arrows like axioms. Then, we deduce new impossibility and possibility results.

Liapunov–Richter theorem in B-convex spaces

Abstract Nonatomic finitely additive correspondences with values in B-convex Banach spaces necessarily have the property that the closure of the range is convex. For this one assumes that the correspondences are of bounded variation.