Abstract
We introduce a new bargaining set for cooperative games in characteristic function form, and investigate its structure and properties. We prove that the new bargaining set is not empty. In fact, we show that it contains the kernel and is contained in the classical bargaining set \({\mathcal{M}^i_1}\), and we further prove that it consists of the unique symmetric vector for the class of simple majority games.
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Michael Maschler was intrigued by the reactive bargaining concept, which was introduced in my unpublished paper (Granot (1994)). Accordingly, in one of his many visits to UBC, he wanted to compare and contrast the outcomes and insights it provides with those provided by the kernel and the classical bargaining set for some well known examples considered in the literature, including the Five Person Market Game example he analyzed in his paper in JET, 1976, where he has demonstrated an advantage of the (classical) bargaining set over the core, and the Seven Person Projective Game, first introduced by von Neumann and Morgenstern. So, we set about to study these examples, and, as usual, the focus was expanded, resulting with our joint paper in IJGT in 1997. In view of the interest my unpublished paper has generated, and its relevance to Michael’s work on the classical bargaining set and the kernel, I am delighted that a shorter version of it is appearing in an issue dedicated to Michael.
Research was partially supported by Natural Sciences and Engineering Research Council grant A4181.
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Granot, D. The reactive bargaining set for cooperative games. Int J Game Theory 39, 163–170 (2010). https://doi.org/10.1007/s00182-009-0201-6
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DOI: https://doi.org/10.1007/s00182-009-0201-6