ON THE SENSITIVITY OF VONNEUMANN AND MORGENSTERN ABSTRACT STABLE SETS - THE STABLE AND THE INDIVIDUAL STABLE BARGAINING SET

The purpose of this paper is twofold: First, to study the properties of the notions of the "stable" and "individual stable" bargaining sets (SBS and ISBS). Second, to point out the sensitivity of the von Neumann and Morgenstern (vN&M) abstract stable set to the dominance relation that is being employed: Insisting that each member of the coalition be made better off yields the SBS, while requiring that at least one member of the coalition is better off and all others are not worse off yields the ISBS. Rather surprisingly, the SBS and the ISBS may have an empty intersection. We fully characterize both the SBS and the ISBS in 3-person games with transferable utilities, and we also show that in ordinally convex games these two sets coincide with the core. As a by-product we thus derive a new proof that such games have a nonempty core. The paper concludes with an open question.