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Title: Intra Firm Bargaining and Shapley Values

Author(s): Björn Brügemann, Pieter A. Gautier and Guido Menzio

Publication Date: August 2015

Keyword(s): intra firm bargaining and Shapley value

Programme Area(s): Industrial Organization, International Macroeconomics and Finance, Labour Economics and Macroeconomics and Growth

Abstract: 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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Bibliographic Reference

Brügemann, B, Gautier, P and Menzio, G. 2015. 'Intra Firm Bargaining and Shapley Values'. London, Centre for Economic Policy Research. http://www.cepr.org/active/publications/discussion_papers/dp.php?dpno=10794