Disadvantageous Syndicates and Stable Cartels: the Case of the Nucleolus

This paper considers a bilateral market with two complementary commodities and gives a rationale for Aumann's paradox. The relationship between the notion of strong stability of a syndicate, i.e., the property that no group of players wants to exit or to enter the syndicate, and the notion of disadvantageous syndicates is summarized in two results. If the two sides of the market are balanced in terms of endowments, every syndicate is strongly stable. If the two sides of the market are not balanced in terms of endowments, then being advantageous, in Aumann's definition, is necessary and sufficient for a syndicate to be strongly stable.