Backward induction foundations of the Shapley value

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We present a noncooperative game model of coalitional bargaining, closely based on that of Gul (1989) but solvable by backward induction. In this game, Gul's condition of “value additivity” does not suffice to ensure the existence of a subgame perfect Nash equilibrium that supports the Shapley value, but a related condition—“no positive value-externalities”—does. Multiple equilibria can arise only in the event of ties, and with a mild restriction on tie-break rules these equilibria all support the Shapley value.
Original languageEnglish
Pages (from-to)2265–2280
Number of pages16
Issue number6
Early online date9 Nov 2016
Publication statusPublished - Nov 2016


  • Shapley value
  • Nash program
  • noncooperative coalitional bargaining

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