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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.

Suggested Citation

  • Predtetchinski, Arkadi, 2011. "One-dimensional bargaining," Games and Economic Behavior, Elsevier, vol. 72(2), pages 526-543, June.
  • Handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:526-543

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    References listed on IDEAS

    1. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    2. 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.
    3. 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.
    4. Olivier Compte & Philippe Jehiel, 2010. "Bargaining and Majority Rules: A Collective Search Perspective," Journal of Political Economy, University of Chicago Press, vol. 118(2), pages 189-221, April.
    5. Predtetchinski Arkadi, 2010. "One-dimensional bargaining: a revision," Research Memorandum 031, 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 371-399, March.
    7. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
    8. Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 309-329, June.
    9. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
    10. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    11. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    12. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(01), pages 73-88, March.
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    Cited by:

    1. Masanori Mitsutsune & Takanori Adachi, 2014. "Estimating noncooperative and cooperative models of bargaining: an empirical comparison," Empirical Economics, Springer, vol. 47(2), pages 669-693, September.
    2. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    3. Daniel Cardona & Clara Ponsatí, 2014. "Super-Majorites, One-Dimensional Policies, and Social Surplus," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(6), pages 884-898, December.
    4. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2011. "On the asymptotic uniqueness of bargaining equilibria," Economics Letters, Elsevier, vol. 111(3), pages 243-246, June.
    5. Daniel Cardona & Arnold Polanski, 2013. "Voting rules and efficiency in one-dimensional bargaining games with endogenous protocol," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 217-240, July.
    6. Clara Ponsatí & Daniel Cardona, 2008. "Bargaining one-dimensional policies and the efficiency of super majority rules," UFAE and IAE Working Papers 762.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    7. Le Breton, Michel & Thomas, Alban & Zaporozhets, Vera, 2012. "Bargaining in River Basin Committees: Rules Versus Discretion," TSE Working Papers 12-324, Toulouse School of Economics (TSE).
    8. P. Herings & Arkadi Predtetchinski, 2015. "Procedural fairness and redistributive proportional tax," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 333-354, June.
    9. Cardona, Daniel & Ponsati, Clara, 2011. "Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules," Games and Economic Behavior, Elsevier, vol. 73(1), pages 65-75, September.


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