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Finite Horizon Bargaining and the Consistent Field

  • Armando Gomes

    (Univeristy of Pennsylvania)

  • Sergiu Hart

    (The Hebrew University of Jerusalem)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Barcelona)

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 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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Paper provided by EconWPA in its series Game Theory and Information with number 9705003.

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Date of creation: 07 May 1997
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Handle: RePEc:wpa:wuwpga:9705003
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  1. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
  2. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  3. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  4. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Harsanyi Values of Large Economies: Nonequivalence to Competitive Equilibria," Games and Economic Behavior, Elsevier, vol. 13(1), pages 74-99, March.
  5. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  6. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
  7. Hart, Oliver D. & Moore, John, 1990. "Property Rights and the Nature of the Firm," Scholarly Articles 3448675, Harvard University Department of Economics.
  8. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  11. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
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