Maria Gabriella Graziano

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.

Cone conditions in oligopolistic market models

Abstract In oligopolistic economic models the presence of big traders on the market determines the lack of perfect competition, then the failure of the Core–Walras equivalence theorem. We show that assuming the ‘big’ agents to have the same economic characteristics, all core allocations are competitive. We allow for the presence of infinitely many commodities; this forces us to make additional assumptions on the commodity space in order to compensate the possible emptiness of the interior of its positive cone. If preferences are convex, a suitable nonatomic economy canonically associated to the model gives an interpretation of the results.

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.

Equilibria in infinite-dimensional production economies with convexified coalitions

Summary. This paper deals with a private ownership production economy assuming that the commodity space is infinite-dimensional. It is first showed that the fuzzy core allocations, a concept that goes back to J.-P. Aubin, are in a one-to-one correspondence with certain core allocations of a continuum economy suitably defined. This result is obtained under convexity of preferences and production sets and separability of the commodity space. In the case of nonconvex preferences and production sets, the set of fuzzy coalitions can be enlarged in order to obtain that every allocation of the core accordingly defined is supported by a non zero price. The proof of the equivalence result when the positive cone of the commodity space has the empty interior, is obtained under assumptions of properness for preferences relations and production sets.

Linear Cost Share Equilibria and the Veto Power of the Grand Coalition

We consider pure exchange economies with finitely many private goods involving the choice of a public project. We discuss core-equivalence results in the general framework of non-Euclidean representation of the collective goods. We define a contribution scheme to capture the fraction of the total cost of providing the project that each blocking coalition is expected to cover. We show that for each given contribution scheme defined over the wider class of Aubin coalitions, the resulting core is equivalent to the corresponding linear cost share equilibria. We also characterize linear cost share equilibria in terms of the veto power of the grand coalition. It turns out that linear cost share equilibria are exactly those allocations that cannot be blocked by the grand coalition with reference to auxiliary economies with the same space of agents and modified initial endowments and cost functions. Unlike the Aubin-type equivalence and results presented in Diamantaras and Gilles (Soc Choice Welf 15:121–139, 1998), this characterization does not depend on a particular contribution scheme.

Economies With Public Projects: Efficiency And Decentralization

The article deals with the two fundamental theorems of welfare economics for production economies with a finite set of agents, infinitely many private goods, and a set of public projects. The problem of efficiency and decentralization is addressed under the following very general assumptions: (a) the commodity-price duality is endowed with a consistent locally convex topology; (b) the set of public projects is without any mathematical structure. Moreover, any agent is characterized by a nonordered preference relation depending on consumption goods and public projects. Approximate and exact welfare theorems are discussed throughout the article. Copyright 2007 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

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.