IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v145y2010i1p189-215.html
   My bibliography  Save this article

One-dimensional bargaining with Markov recognition probabilities

Author

Listed:
  • Herings, P. Jean-Jacques
  • Predtetchinski, Arkadi

Abstract

We study a process of bargaining over alternatives represented by points in the unit interval. The paper focuses on the asymptotic behavior of the subgame perfect equilibrium in stationary strategies as the continuation probability approaches one. We give a complete characterization of the limit of the equilibrium proposals as the generalized fixed point of the decumulative distribution of the players' ideal points as induced by the recognition probabilities. In contrast to the existing literature, we find no general relationship between the limit equilibrium proposals and either the Nash bargaining solution or the median voter outcome.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:189-215
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(09)00116-1
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, 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. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. repec:cup:apsrev:v:83:y:1989:i:04:p:1181-1206_08 is not listed on IDEAS
    5. Brian Knight, 2005. "Estimating the Value of Proposal Power," American Economic Review, American Economic Association, vol. 95(5), pages 1639-1652, December.
    6. Haller, Hans, 1986. "Non-cooperative bargaining of N [ges] 3 players," Economics Letters, Elsevier, vol. 22(1), pages 11-13.
    7. 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.
    8. Cho, Seok-ju & Duggan, John, 2009. "Bargaining foundations of the median voter theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 851-868, March.
    9. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    10. P. Herings & Arkadi Predtetchinski, 2012. "Sequential share bargaining," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 301-323, May.
    11. 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.
    12. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
    13. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    14. 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.
    15. Tasos Kalandrakis, 2004. "Proposal Rights and Political Power," Wallis Working Papers WP38, University of Rochester - Wallis Institute of Political Economy.
    16. Thomas Romer & Howard Rosenthal, 1978. "Political resource allocation, controlled agendas, and the status quo," Public Choice, Springer, vol. 33(4), pages 27-43, December.
    17. 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.
    18. 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.
    19. Eraslan, Hulya, 2002. "Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model," Journal of Economic Theory, Elsevier, vol. 103(1), pages 11-30, March.
    20. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
    21. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yamaguchi, Kazuo, 2011. "Location of an undesirable facility on a network: A bargaining approach," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 104-108, September.
    2. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2011. "On the asymptotic uniqueness of bargaining equilibria," Economics Letters, Elsevier, vol. 111(3), pages 243-246, June.
    3. Herings P.J.J. & Houba H, 2015. "Costless delay in negotiations," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    4. 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.
    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. Predtetchinski, Arkadi, 2011. "One-dimensional bargaining," Games and Economic Behavior, Elsevier, vol. 72(2), pages 526-543, June.
    7. Houba, Harold & van der Laan, Gerard & Zeng, Yuyu, 2014. "Asymmetric Nash Solutions in the River Sharing Problem," Strategic Behavior and the Environment, now publishers, vol. 4(4), pages 321-360, December.
    8. P. Jean-Jacques Herings & A. Predtetchinski, 2016. "Bargaining under monotonicity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 221-243, June.
    9. P. Herings & Arkadi Predtetchinski, 2012. "Sequential share bargaining," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 301-323, May.
    10. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    11. repec:eee:gamebe:v:103:y:2017:i:c:p:185-198 is not listed on IDEAS
    12. Jan Zapal, 2014. "Simple Markovian Equilibria in Dynamic Spatial Legislative Bargaining," CERGE-EI Working Papers wp515, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    13. Klaus Kultti & Hannu Vartiainen, 2010. "Multilateral non-cooperative bargaining in a general utility space," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 677-689, October.
    14. Herings P. Jean-Jacques & Predtetchinski Arkadi, 2011. "Procedurally Fair Taxation," Research Memorandum 024, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Herings P.J.J. & Meshalkin A. & Predtetchinski A., 2012. "A Folk Theorem for Bargaining Games," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. 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.

    More about this item

    Keywords

    One-dimensional bargaining Markov process Median voter theorem Nash bargaining solution;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:189-215. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.