Edgeworth equilibria, fuzzy core, and equilibria of a production economy without ordered preferences

The Veto Mechanism Revisited

“…Following García and Hervés (1993), we interpret a continuum economy with n types of agents as an economy with n agents. In this way, we extend and generalize some results in Florenzano (1990) and Hüsseinov (1994), while obtaining other new characterizations of the core and Edgeworth equilibrium. We make clear the power of the pondered veto mechanism showing that it is enough to consider the coalition of all agents as an admissible coalition, in order to guarantee that the only allocations which are not blocked by the pondered veto system are just the Walrasian allocations.…”

“…Moreover, Caratheodory's theorem allows us to conclude that it is enough to consider the pondered veto mechanism until the ( + 1)-fold replica economy, in order to get the set of Edgeworth equilibria or, alternatively, the set of Walrasian allocations for the economy E n . Florenzano (1990) shows the existence of Walrasian equilibrium, fuzzy core and Edgeworth equilibrium of a production economy without ordered preferences. Both the restricted and pondered veto mechanism may be analyze within the non ordered preference set up.…”

Production equilibria in vector lattices

“…Following Aliprantis et al ([3], [4], [5]), x ∈ A X (E) is said to be an Edgeworth equilibrium if, for every integer r ≥ 1, the r-repetition of x belongs to the core of the r-replication of E. Let C e (E) denote the set of all Edgeworth equilibria of E. As it is easily seen and proved in Florenzano [15], under convexity assumptions for consumption and production sets, the set of all Edgeworth equilibria C e (E) contains the set C f (E) of all x ∈ A X (E) such that there exists no t = (t i ) ∈ [0, 1] I , t = 0, and no x t ∈ t i >0 X i satisfying…”

“…Here, as in Mas-Colell and Richard [21], Richard [25] and many others papers ( [10], [23], [1], [26], [27], [13], [18]), we assume that the commodity space is a vector lattice whose topological dual is a sublattice of its order dual. As well-known, this setting, which covers most of the important infinite dimensional models, was introduced in order to include the models of commodity differentiation in Jones [17] and of intertemporal consumption in Huang and Kreps [16], not covered before by a number of equilibrium existence results (e.g., [19], [29], [30], [24], [4], [5], [15], [28]) requiring that the commodity space be a topological vector lattice. Even if it leaves out of its scope some commodity-price dualities of economic interest (a detailed discussion on relevant commodity-price dualities can be found in [3], [22]), such a setting is also the most general one used by now in equilibrium existence proofs, if one excepts a thought provoking paper by Aliprantis et al [8] discarding the vector lattice property of the commodity space and its dual at the cost of an alternate theory of value with non-linear prices.…”

Equilibrium Analysis in Kantorovich Spaces

“…However the conditions under which fuzzy core is nonempty are well known in literature (e.g., see [14], [13]) so taking them and adding the requirement of nontrivial E-properness we obtain an existence theorem of nontrivial quasiequilibria. We would like to recall further important Riesz-Kantorovich formula on the presentation of supremum of linear functionals in linear vector lattice.…”