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Simultaneous Nash Bargaining with Consistent Beliefs

  • Roberto Burguet and Ramon Caminal

We propose and analyze a new solution concept, theR-solution, for three-person, transferable utility, cooperative games. In the spirit of the Nash Bargaining Solution, our concept is founded on the predicted outcomes of simultaneous, two-party negotiations that would be the alternative to the grand coalition. These possibly probabilistic predictions are based on consistent beliefs. We analyze the properties of theR-solution and compare it with the Shapley value and other concepts. The R-solution exists and is unique. It belongs to the bargaining set and to the core whenever the latter is not empty. In fact, when the grand coalition can simply execute one of the three possible bilateral trades, the R-solution is the most egalitarian selection of the bargaining set. Finally, we discuss how theR-solution changes important conclusions of several well known Industrial Organization models.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 521.

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Date of creation: Nov 2010
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Handle: RePEc:bge:wpaper:521
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  1. Horn, Henrik & Persson, Lars, 1996. "Endogenous Mergers in Concentrated Markets," CEPR Discussion Papers 1544, C.E.P.R. Discussion Papers.
  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. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  4. repec:oup:qjecon:v:113:y:1998:i:2:p:361-386 is not listed on IDEAS
  5. Serrano, Roberto & Shimomura, Ken-Ichi, 1998. "Beyond Nash Bargaining Theory: The Nash Set," Journal of Economic Theory, Elsevier, vol. 83(2), pages 286-307, December.
  6. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-64, November.
  7. Sven-Olof Fridolfsson & Johan Stennek, 2001. "Why Mergers Reduce Profits and Raise Share Prices: A Theory of Preemptive Mergers," CIG Working Papers FS IV 01-26, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
  8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  9. Winter, Eyal, 2002. "The shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 53, pages 2025-2054 Elsevier.
  10. David de Meza & Mariano Selvaggi, 2004. "Exclusive Contracts Foster Relationship-Specific Investment," The Centre for Market and Public Organisation 04/105, Department of Economics, University of Bristol, UK.
  11. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Post-Print halshs-00754423, HAL.
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