Finite Horizon Bargaining and the Consistent Field
AbstractThis 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 field 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. Journal of Economic Literature Classification Numbers: C71, C72.
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Date of creation: 07 May 1997
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Other versions of this item:
- Gomes, Armando & Hart, Sergiu & Mas-Colell, Andreu, 1999. "Finite Horizon Bargaining and the Consistent Field," Games and Economic Behavior, Elsevier, vol. 27(2), pages 204-228, May.
- Armando Gomes & Sergiu Hart & Andreu Mas-Colell, 1997. "Finite horizon bargaining and the consistent field," Economics Working Papers 241, Department of Economics and Business, Universitat Pompeu Fabra.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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