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Finite Horizon Bargaining and the Consistent Field

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

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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  • 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.
    • Handle: RePEc:eee:gamebe:v:27:y:1999:i:2:p:204-228
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    References listed on IDEAS

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    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 1119-1158, December.
    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.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
    5. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    6. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    7. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 255-273, March.
    8. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
    9. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    10. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
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    Citations

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    Cited by:

    1. 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.
    2. Armando Gomes, "undated". "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.
    3. Emililo Calvo, 2004. "Single NTU-value solutions," Game Theory and Information 0405004, University Library of Munich, Germany, revised 10 Jun 2004.
    4. Armo Gomes, "undated". "A Theory of Negotiation and Formation of Coalition," Penn CARESS Working Papers f0f956747161c96ffb6e79d05, Penn Economics Department.
    5. Joan-Maria Esteban & József Sákovics, 2005. "A Theory of Agreements in the Shadow of Conflict," Working Papers 255, Barcelona School of Economics.
    6. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 603-622, August.
    7. 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.

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    More about this item

    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

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