Working Paper: CEPR ID: DP10794
Authors: Bjrn Brgemann; Pieter A. Gautier; Guido Mennzio
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.
Keywords: intra-firm bargaining; Shapley value
JEL Codes: D21; J30
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Bargaining process (C78) | Wage structure (J31) |
| Worker's position in bargaining order (J52) | Wage outcomes (J31) |
| Wage profile of SZ game (J31) | Distribution of wages (J31) |
| Rolodex game conditions (C72) | Unique subgame perfect equilibrium (C72) |
| Worker's rejection of counteroffer (J52) | Position in bargaining order (C78) |
| Rolodex game (C72) | Wages equal to Shapley values (J31) |