The Weak Core, Partition‐Based Universal Stability, and Their Risk Associations Through A Partial Order

We are concerned with the stability of a transferable‐utility cooperative (TU) game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings. This principle of consensual blocking , as well as the traditional core‐defining one of unilateral blocking and one straddling in between, can then be applied to partition‐allocation pairs . Each such pair is made up of a partition of the grand coalition and a corresponding allocation vector whose components are efficient and individually rational for the various constituent coalitions of the given partition. Among the resulting stability concepts, two are universal in that any game has stable solutions. For a game with strictly positive values, furthermore, its imputations possess fractional interpretations. These would allow a certain ranking between games, in what we call “ centripetality ”, to imply a clearly describable shift in the games' stable solutions. When coalitions' values are built on both random outcomes and a common positively‐homogeneous law‐invariant reward function characterizing players' enjoyments from their shares, such comparative statics can help explain the phenomenon that aversion to risk promotes cooperation . Our results can have direct impacts on operations management settings like inventory centralization.