DP10794 Intra Firm Bargaining and Shapley Values

Author(s): Björn Brügemann, Pieter A. Gautier, Guido Menzio
Publication Date: August 2015
Keyword(s): intra firm bargaining, Shapley value
JEL(s): D21, J30
Programme Areas: Labour Economics, Industrial Organization, International Macroeconomics and Finance, Macroeconomics and Growth
Link to this Page: www.cepr.org/active/publications/discussion_papers/dp.php?dpno=10794

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.