Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2016, Volume 84, Issue 6

Backward Induction Foundations of the Shapley Value
p. 2265-2280

Ben McQuillin, Robert Sugden

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.

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