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

Author

Listed:
  • Natalia Naumova

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

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.

Suggested Citation

  • Natalia Naumova, 2020. "Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-23, September.
    • Handle: RePEc:wsi:igtrxx:v:22:y:2020:i:03:n:s0219198920500012
    DOI: 10.1142/S0219198920500012
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