Learning from a Piece of Pie: The Empirical Content of Nash Bargaining

Learning from a Piece of Pie: The Empirical Content of Nash Bargaining Consider a model of bargaining, in which two players, 1 and 2, share a pie of size y. The bargaining environment is described by a set of parameters λ that may affect agents’ preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither the agents’ utilities nor their threat points. Assuming that the agents adopt a Nash bargaining solution, we investigate the empirical content of this assumption. We first show that in the most general framework, any outcome can be rationalized as a Nash solution. However, if (i) the size of the pie y does not influence the players’ threat points and (ii) there exist (at least) two parameters λ1 and λ2 that are player-specific, in the sense that λi does not influence the utility or the threat point of player j ≠ i, then Nash bargaining generates strong testable restrictions. Moreover, the underlying structure of the bargaining, i.e., the players’ utility and threat point functions, can be recovered under slightly more demanding conditions. JEL Classification: C71, C78 Keywords: bargaining game, Nash solution, testability, identifiability, cardinal utility Corresponding author: Olivier Donni University of Cergy-Pontoise 33, Boulevard du Port 95011 Cergy-Pontoise Cedex France Email: [email protected] * Paper presented at seminars in Chicago and Paris. We thank participants, and in particular Jaap Abbring, Bernard Fortin and Jim Heckman for useful comments and suggestions. Financial support from the NSF (grant) and the FQRSC is gratefully acknowledged. Errors are ours. I passed by his garden, and marked, with one eye, How the Owl and the Panter were sharing a pie: The Panther took pie-crust, and gravy, and meat, While the Old had the dish as its share of the treat. When the pie was all …nished, the Owl, as a boon, Was kindly permitted to pocket the spoon: While the Panther received knife and fork with a growl, And concluded the banquet by... Lewis Caroll (Alice’s Adventures in Wonderland, 1866)