Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation

Natalia Naumova ()
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Natalia Naumova: Faculty of Mathematics and Mechanics, St.Petersburg State University, Universitetsky pr. 28, Petrodvorets, St.Petersburg, Russia

International Game Theory Review (IGTR), 2020, vol. 22, issue 03, 1-23

Abstract: Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions 𠒜 and can use coalitions from ℬ⊃𠒜. Necessary and sufficient conditions on 𠒜, ℬ that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game (N,v) with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if |N|≤ 4 and ℬ = 2N. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author.For monotonic ℬ, the condition on 𠒜 for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for |N|≤ 6.

Keywords: Cooperative game; bargaining set; reactive bargaining set; semi-reactive bargaining set; kernel (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219198920500012

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