A collection B of coalitions is balanced if and only if there exists positive weights {λS : S ˆˆ B} such that

where eS is the characteristic vector of the coalition S (example 3.19) and gS: X †’ „œ represents the share of coalition S at the allocation x (example 3.16).
In a natural extension of cohesivity (33) a cooperative game G = (N, w) is balanced if

for every balanced family of coalitions B. Balance is the appropriate necessary and sufficient condition for nonemptyness of the core.

Transcribed Image Text:

Σλ3s ises and gN eN SE SE