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Computation of equilibrium values in the Baron and Ferejohn bargaining model

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  • 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
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    References listed on IDEAS

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    1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    2. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    3. 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.
    4. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    5. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    6. 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.
    7. Tasos Kalandrakis, 2006. "Proposal Rights and Political Power," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 441-448, April.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    13. 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.
    14. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    15. Winter, Eyal, 1996. "Voting and Vetoing," American Political Science Review, Cambridge University Press, vol. 90(4), pages 813-823, December.
    16. 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.
    17. 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.
    18. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
    19. R. Saigal, 1976. "On Paths Generated by Fixed Point Algorithms," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 359-380, November.
    20. 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.
    21. 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.
    22. 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.
    23. Haruo Imai & Hannu Salonen (corresponding author), 2012. "Bargaining and Rent Seeking," Discussion Papers 80, Aboa Centre for Economics.
    24. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    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.
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    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. Imai, Haruo, 2024. "Bargaining and rent seeking: Asymmetric equilibria with two investment levels," Economics Letters, Elsevier, vol. 240(C).
    4. 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.
    5. 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.
    6. Evdokimov, Kirill S., 2023. "Equality in legislative bargaining," Journal of Economic Theory, Elsevier, vol. 212(C).
    7. 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.

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    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

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