Credible Coalitions and the Core 1

; A problem with the concept of the core is that it does not explicitly capture the credibility of blocking coalitions, This notion is defined, and the concept of a modified core introduced, consisting of allocations not blocked by any credible coalition. The core and modified core are then shown to be identical. The concept of credibility is thus implicit in the definition of the core. Consider a cooperative game in characteristic function form (see, e.g. Aumann 1967). N = { I, ..., n} is the player set. With each S ~ N, the characteristic function v(.) associates a nonempty subset v(S) of Rs .3 ut H ~ v(N) be the set of outcomes that can actually occur; it has, at least, the property that v(N) = {x E RN /there isy EHwithy ~x} (1) Cooperative games with side payments and transferable utility form a special case, with v(S) = {x E Rs / ~ Xi ~f(S)} ieS (2) where f(o) is the NM characteristic function.