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Finite Horizon Bargaining and the Consistent Field

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Author Info
Armando Gomes (Univeristy of Pennsylvania)
Sergiu Hart (The Hebrew University of Jerusalem)
Andreu Mas-Colell (Universitat Pompeu Fabra, Barcelona)

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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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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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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Hart, Oliver & Moore, John, 1990. "Property Rights and the Nature of the Firm," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1119-58, December. [Downloadable!] (restricted)
    Other versions:
  2. 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. [Downloadable!] (restricted)
    Other versions:
  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. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  5. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June. [Downloadable!] (restricted)
  6. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January. [Downloadable!] (restricted)
  7. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March. [Downloadable!] (restricted)
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  8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  9. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
  10. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics. [Downloadable!]
  11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Armo Gomes, . "A Theory of Negotiation and Formation of Coalition," Penn CARESS Working Papers f0f956747161c96ffb6e79d05, Penn Economics Department. [Downloadable!]
  2. Armando Gomes, . "A Theory of Negotiations and Formation of Coalitions," Rodney L. White Center for Financial Research Working Papers 21-99, Wharton School Rodney L. White Center for Financial Research. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
  4. Emililo Calvo, 2004. "Single NTU-value solutions," Game Theory and Information 0405004, EconWPA, revised 10 Jun 2004. [Downloadable!]
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