Price characterization of stable allocations in exchange economies with externalities

A pure exchange economy where the consumers have utility functions U_i(v₁(x₁),…, v_m(x_m)) for i = 1,…, m and where x_j is the consumption of consumer j, is studied. U_i may be nonincreasing or nondecreasing in v_j for j ≠ i. i is said to be nonbenevolent or nonmalevolent towards j, accordingly.An allocation is stable if no coalition can redistribute what it receives in the allocation to get an allocation which is preferred, given the consumptions of the consumers in the complementary coalition. Results concerning the relation among the Paretooptimal, stable and equilibrium allocations (under different definitions of equilibrium) are given. In particular, it turns out that in case every consumer is non-benevolent towards every other consumer, the classical results, concerning the relation between Paretooptimal allocations and equilibrium allocations, can be generalized in a satisfactory way.