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One-dimensional bargaining

  • Predtetchinski, Arkadi

We study a model of multilateral bargaining over social outcomes represented by the points in the unit interval. The acceptance or rejection of a proposal is determined by an acceptance rule represented by the collection of decisive coalitions. The focus of the paper is on the asymptotic behavior of subgame perfect equilibria in stationary strategies as the players become infinitely patient. We show that, along any sequence of stationary subgame perfect equilibria the social acceptance set collapses to a point. This point, called the limit of bargaining equilibria, is independent of the sequence of equilibria and is uniquely determined by the set of players, the utility functions, the recognition probabilities, and the acceptance rule. The central result of the paper is a characterization of the limit of bargaining equilibria as a unique zero of the characteristic equation.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 72 (2011)
Issue (Month): 2 (June)
Pages: 526-543

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Handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:526-543
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  1. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  2. Eraslan, H. & Merlo, A., 2000. "Majority Rule in a Stochastic Model of Bargaining," Working Papers 00-05, C.V. Starr Center for Applied Economics, New York University.
  3. Predtetchinski Arkadi, 2010. "One-dimensional bargaining: a revision," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Philippe Jehiel & Oliver Compte, 2007. "Bargaining and Majority Rules: A Collective Search Perspective," Levine's Bibliography 843644000000000131, UCLA Department of Economics.
  5. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2007. "One-dimensional Bargaining with Markov Recognition Probabilities," Research Memorandum 044, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
  7. Seok-ju Cho & John Duggan, 2001. "Uniqueness of Stationary Equilibria in a one-Dimensional Model of Bargaining," Wallis Working Papers WP23, University of Rochester - Wallis Institute of Political Economy.
  8. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
  9. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.
  10. Imai, Haruo & Salonen, Hannu, 2000. "The representative Nash solution for two-sided bargaining problems," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 349-365, May.
  11. Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer, vol. 28(2), pages 309-329, 06.
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