IDEAS home Printed from https://ideas.repec.org/p/roc/wallis/wp65.html
   My bibliography  Save this paper

Computation of equilibrium values in the Baron and Ferejohn bargaining model

Author

Listed:
  • Tasos Kalandrakis

    (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158)

Abstract

Computation of exact equilibrium values for n-player divide-the-dollar legislative bargaining games as in Baron and Ferejohn (1989) with general quota voting rules, recognition probabilities, and discount factors, can be achieved by solving at most n bivariate square linear systems of equations. This approach recovers Eraslan's (2002) uniqueness result and relies on a characterization of equilibria in terms of two variables that satisfy a pair of piecewise linear equations.

Suggested Citation

  • Tasos Kalandrakis, 2014. "Computation of equilibrium values in the Baron and Ferejohn bargaining model," Wallis Working Papers WP65, University of Rochester - Wallis Institute of Political Economy.
    • Handle: RePEc:roc:wallis:wp65
    as

    Download full text from publisher

    File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_65.pdf
    File Function: full text
    Download Restriction: None
    ---><---

    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. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    3. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954, Decembrie.
    4. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    5. Diermeier, Daniel & Feddersen, Timothy J., 1998. "Cohesion in Legislatures and the Vote of Confidence Procedure," American Political Science Review, Cambridge University Press, vol. 92(3), pages 611-621, September.
    6. Tasos Kalandrakis, 2006. "Proposal Rights and Political Power," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 441-448, April.
    7. Roger B. Myerson & Daniel Diermeier, 1999. "Bicameralism and Its Consequences for the Internal Organization of Legislatures," American Economic Review, American Economic Association, vol. 89(5), pages 1182-1196, December.
    8. James M. Snyder Jr. & Michael M. Ting & Stephen Ansolabehere, 2005. "Legislative Bargaining under Weighted Voting," American Economic Review, American Economic Association, vol. 95(4), pages 981-1004, September.
    9. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 193-236, January.
    10. 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.
    11. 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.
    12. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    13. Winter, Eyal, 1996. "Voting and Vetoing," American Political Science Review, Cambridge University Press, vol. 90(4), pages 813-823, December.
    14. Ansolabehere, Stephen & Snyder, James M. & Ting, Michael M., 2003. "Bargaining in Bicameral Legislatures: When and Why Does Malapportionment Matter?," American Political Science Review, Cambridge University Press, vol. 97(3), pages 471-481, August.
    15. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, vol. 61(2), pages 290-301, December.
    16. R. Saigal, 1976. "On Paths Generated by Fixed Point Algorithms," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 359-380, November.
    17. 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.
    18. McCarty, Nolan M., 2000. "Presidential Pork: Executive Veto Power and Distributive Politics," American Political Science Review, Cambridge University Press, vol. 94(1), pages 117-129, March.
    19. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    20. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    21. B. Curtis Eaves & Herbert Scarf, 1976. "The Solution of Systems of Piecewise Linear Equations," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 1-27, February.
    22. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
    23. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(1), pages 73-88, March.
    24. Haruo Imai & Hannu Salonen (corresponding author), 2012. "Bargaining and Rent Seeking," Discussion Papers 80, Aboa Centre for Economics.
    25. 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.
    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. Miller, Luis & Montero, Maria & Vanberg, Christoph, 2018. "Legislative bargaining with heterogeneous disagreement values: Theory and experiments," Games and Economic Behavior, Elsevier, vol. 107(C), pages 60-92.
    2. Jiawei Li & Tianxiang Cui & Graham Kendall, 2022. "Equilibrium in a Bargaining Game of Two Sellers and Two Buyers," Mathematics, MDPI, vol. 10(15), pages 1-9, July.
    3. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    4. Andrzej Baranski & Ernesto Reuben, 2023. "Competing for Proposal Rights: Theory and Experimental Evidence," Working Papers 20220085, New York University Abu Dhabi, Department of Social Science, revised Mar 2023.
    5. Evdokimov, Kirill S., 2023. "Equality in legislative bargaining," Journal of Economic Theory, Elsevier, vol. 212(C).
    6. Hülya Eraslan, 2016. "Uniqueness of stationary equilibrium payoffs in the Baron–Ferejohn model with risk-averse players," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 29-40, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    2. James M. Snyder Jr. & Michael M. Ting & Stephen Ansolabehere, 2005. "Legislative Bargaining under Weighted Voting," American Economic Review, American Economic Association, vol. 95(4), pages 981-1004, September.
    3. Juan Ortner, 2014. "Political Bargaining in a Changing World," 2014 Meeting Papers 445, Society for Economic Dynamics.
    4. Zapal, Jan, 2020. "Simple Markovian equilibria in dynamic spatial legislative bargaining," European Journal of Political Economy, Elsevier, vol. 63(C).
    5. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    6. Montero, Maria, 2017. "Proportional Payoffs in Legislative Bargaining with Weighted Voting: A Characterization," Quarterly Journal of Political Science, now publishers, vol. 12(3), pages 325-346, October.
    7. Ortner, Juan, 2017. "A theory of political gridlock," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    9. Le Breton, Michel & Thomas, Alban & Zaporozhets, Vera, 2012. "Bargaining in River Basin Committees: Rules Versus Discretion," LERNA Working Papers 12.12.369, LERNA, University of Toulouse.
    10. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, vol. 6(2), pages 1-18, April.
    11. Tasos Kalandrakis, 2006. "Proposal Rights and Political Power," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 441-448, April.
    12. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    13. Yves Breitmoser, 2011. "Parliamentary bargaining with priority recognition for committee members," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 149-169, June.
    14. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    15. Seok-ju Cho & John Duggan, 2015. "A folk theorem for the one-dimensional spatial bargaining model," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 933-948, November.
    16. Okada, Akira, 2011. "Coalitional bargaining games with random proposers: Theory and application," Games and Economic Behavior, Elsevier, vol. 73(1), pages 227-235, September.
    17. Eraslan, Hülya & Merlo, Antonio, 2017. "Some unpleasant bargaining arithmetic?," Journal of Economic Theory, Elsevier, vol. 171(C), pages 293-315.
    18. Breitmoser, Yves & Tan, Jonathan H.W., 2010. "Generosity in bargaining: Fair or fear?," MPRA Paper 27444, University Library of Munich, Germany.
    19. Drouvelis, Michalis & Montero, Maria & Sefton, Martin, 2010. "Gaining power through enlargement: Strategic foundations and experimental evidence," Games and Economic Behavior, Elsevier, vol. 69(2), pages 274-292, July.
    20. Maria Montero, 2023. "Coalition Formation in Games with Externalities," Dynamic Games and Applications, Springer, vol. 13(2), pages 525-548, June.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:roc:wallis:wp65. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard DiSalvo (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.