Intra Firm Bargaining and Shapley Values

NBER Working Paper No. 21508

Issued in August 2015

NBER Program(s):Economic Fluctuations and Growth



The paper revisits the problem of wage bargaining between a firm and multiple workers. We show that the Subgame Perfect Equilibrium of the extensive-form game proposed by Stole and Zwiebel (1996a) does not imply a profile of wages and profits that coincides with the Shapley values as claimed in their classic paper. We propose an alternative extensive-form bargaining game, the Rolodex Game, that follows a simple and realistic protocol and that, under some mild restrictions, admits a unique Subgame Perfect Equilibrium generating a profile of wages and profits that are equal to the Shapley values. The vast applied literature that refers to the Stole and Zwiebel game to give a game-theoretic foundation to the use of the Shapley values as the outcome of the bargain between a firm and multiple workers should instead refer to the Rolodex game.

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Document Object Identifier (DOI): 10.3386/w21508

Published: Björn Brügemann, Pieter Gautier, Guido Menzio; Intra Firm Bargaining and Shapley Values, The Review of Economic Studies citation courtesy of

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