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Finite Horizon Bargaining and the Consistent Field

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  • Armando Gomes

    (Univeristy of Pennsylvania)

  • Sergiu Hart

    (The Hebrew University of Jerusalem)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Barcelona)

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 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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Bibliographic Info

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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References

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  1. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  2. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  3. 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.
  4. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  5. Hart, Oliver D. & Moore, John, 1990. "Property Rights and the Nature of the Firm," Scholarly Articles 3448675, Harvard University Department of Economics.
  6. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
  7. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  8. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  10. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  11. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
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Cited by:
  1. Joan Esteban & Jozsef Sakovics, 2005. "A theory of agreements in the shadow of conflict," ESE Discussion Papers 139, Edinburgh School of Economics, University of Edinburgh.
  2. Armando Gomes, . "A Theory of Negotiation and Formation of Coalition," CARESS Working Papres 99-12, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  3. Barbera, Salvador & Perea, Andres, 2002. "Supporting others and the evolution of influence," Journal of Economic Dynamics and Control, Elsevier, vol. 26(12), pages 2051-2092, October.
  4. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer, vol. 41(3), pages 603-622, August.
  5. Armo Gomes, . "A Theory of Negotiation and Formation of Coalition," Penn CARESS Working Papers f0f956747161c96ffb6e79d05, Penn Economics Department.
  6. Emililo Calvo, 2004. "Single NTU-value solutions," Game Theory and Information 0405004, EconWPA, revised 10 Jun 2004.
  7. de Clippel, Geoffroy, 2007. "The procedural value for cooperative games with non-transferable utility," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 46-52, January.

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