Equivalence of Competitive Equilibria, Fuzzy Cores, and Fuzzy Bargaining Sets in Finite Production Economies

Abstract

For an exchange economy with a continuum of traders and a finite-dimensional commodity space under some standard assumptions, Aumann showed that the core and the set of competitive allocations (two most important solutions) coincide and Mas-Colell proved that the bargaining set and the set of competitive allocations coincide. However, in the case of exchange economies with a finite number of traders, it is well-known that the set of competitive allocations could be a strict subset of the core which can also be a strict subset of the bargaining set. In this paper, we establish the equivalence of the fuzzy core, the fuzzy bargaining set (or Aubin bargaining set), and the set of competitive allocations in a finite coalition production economy with an infinite-dimensional commodity space under some standard assumptions. We first derive a continuous equivalence theorem and then discretize it to obtain the desired equivalence in finite economies.