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Finite Horizon Bargaining and the Consistent Field

  • Gomes, Armando
  • Hart, Sergiu
  • Mas-Colell, Andreu

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 27 (1999)
Issue (Month): 2 (May)
Pages: 204-228

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Handle: RePEc:eee:gamebe:v:27:y:1999:i:2:p:204-228
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  2. Oliver Hart & John Moore, 1988. "Property Rights and the Nature of the Firm," Working papers 495, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  4. Hart, S. & Mas-Colell, A., 1993. "Harsanyi Values of Large Economies: Non Equivalence to Competitive Equilibria," Harvard Institute of Economic Research Working Papers 9, Harvard - Institute of Economic Research.
  5. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  7. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
  8. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
  9. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  10. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  11. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
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