Working Paper: NBER ID: w21508
Authors: Bjrn Brgemann; Pieter Gautier; Guido Menzio
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: No keywords provided
JEL Codes: D21; J30
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Stole and Zwiebel (SZ) game (C72) | Shapley values (C71) |
| worker position in bargaining order (J52) | wage earned by a worker (J31) |
| worker order in bargaining (C78) | surplus captured by workers (E25) |
| prior agreements (L14) | last worker's wage (J31) |
| Rolodex game (C72) | wages equal to Shapley values (J31) |
| worker position (J29) | gains from trade (F11) |