The proportion of blocking coalitions in atomless economies

In this paper we investigate the number of coalitions that block a given non-competitive allocation. In an atomless economy with a finite number of types we identify coalition with its profile. Considering profiles π that represent coalitions with the same proportions of types as in the whole society, we prove that there is a ball B_π with π as its center so that ‘almost half’ of the profiles in B_π are blocking. This result is an analogous result to that of Mas-Colell (1978) who dealt with large finite markets.