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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: Sep 2015
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Handle: RePEc:bge:wpaper:521
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  1. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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  4. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Post-Print halshs-00754423, HAL.
  5. Sven-Olof Fridolfsson & Johan Stennek, 2005. "Why Mergers Reduce Profits And Raise Share Prices-A Theory Of Preemptive Mergers," Journal of the European Economic Association, MIT Press, vol. 3(5), pages 1083-1104, 09.
  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. Persson, Lars & Horn, Henrik, 1998. "Endogenous Mergers in Concentrated Markets," Working Paper Series 513, Research Institute of Industrial Economics.
  8. 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.
  9. 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.
  10. David De Meza & Ben Lockwood, 1998. "Does Asset Ownership Always Motivate Managers? Outside Options And The Property Rights Theory Of The Firm," The Quarterly Journal of Economics, MIT Press, vol. 113(2), pages 361-386, May.
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