Finite Horizon Bargaining and the Consistent Field

Posted: 5 Aug 2004

See all articles by Armando R. Gomes

Armando R. Gomes

Washington University in St. Louis - John M. Olin Business School; Washington University in Saint Louis - John M. Olin Business School

Sergiu Hart

Hebrew University of Jerusalem - Center for the Study of Rationality

Andreu Mas-Colell

Universitat Pompeu Fabra

Abstract

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show that for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent fields converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.

JEL Classification: C71, C72

Suggested Citation

Gomes, Armando R. and Gomes, Armando R. and Hart, Sergiu and Mas-Colell, Andreu, Finite Horizon Bargaining and the Consistent Field. Available at SSRN: https://ssrn.com/abstract=572641

Armando R. Gomes

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-4569 (Phone)

Washington University in Saint Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-4569 (Phone)

Sergiu Hart

Hebrew University of Jerusalem - Center for the Study of Rationality ( email )

Feldman Building
Givat-Ram
Jerusalem, 91904
Israel
+972-2-6584135 (Phone)
+972-2-6513681 (Fax)

HOME PAGE: http://www.ma.huji.ac.il/~hart

Andreu Mas-Colell (Contact Author)

Universitat Pompeu Fabra ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-3) 542 20 58 (Phone)
(34-3) 542 12 23 (Fax)

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