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Subgame perfect equilibria in majoritarian bargaining

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  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • Meshalkin, A.V.

    (Microeconomics & Public Economics)

  • Predtetchinski, A.

    (Microeconomics & Public Economics)

Abstract

We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory experiments show various deviations from this equilibrium, where different offers are typically made and delay may occur before acceptance. We address the issue to what extent these findings are compatible with subgame perfect equilibrium and characterize the set of subgame perfect equilibrium payoffs for any value of the discount factor. We show that for any proposal in the interior of the space of possible agreements there exists a discount factor such that the proposal is made and accepted. We characterize the values of the discount factor for which equilibria with one-period delay exist. We show that any amount of equilibrium delay is possible and we construct subgame perfect equilibria such that arbitrary long delay occurs with probability one.

Suggested Citation

  • Herings, P.J.J. & Meshalkin, A.V. & Predtetchinski, A., 2013. "Subgame perfect equilibria in majoritarian bargaining," Research Memorandum 072, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013072
    DOI: 10.26481/umagsb.2013072
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. John Kagel & Hankyoung Sung & Eyal Winter, 2010. "Veto power in committees: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 13(2), pages 167-188, June.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    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. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-924, July.
    6. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters, in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111, World Scientific Publishing Co. Pte. Ltd..
    7. Luis Miller & Christoph Vanberg, 2013. "Decision costs in legislative bargaining: an experimental analysis," Public Choice, Springer, vol. 155(3), pages 373-394, June.
    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. Bradfield, Anthony J. & Kagel, John H., 2015. "Legislative bargaining with teams," Games and Economic Behavior, Elsevier, vol. 93(C), pages 117-127.
    10. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    11. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    12. Herings, P. Jean-Jacques & Meshalkin, Andrey & Predtetchinski, Arkadi, 2017. "A one-period memory folk theorem for multilateral bargaining games," Games and Economic Behavior, Elsevier, vol. 103(C), pages 185-198.
    13. Duozhe Li, 2014. "Multiplicity of Equilibrium Payoffs in Three-Player Baron-Ferejohn Model," Economics Bulletin, AccessEcon, vol. 34(2), pages 1122-1132.
    14. 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.
    15. Andrzej Baranski & John H. Kagel, 2015. "Communication in legislative bargaining," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 1(1), pages 59-71, July.
    16. Fréchette, Guillaume R. & Kagel, John H. & Lehrer, Steven F., 2003. "Bargaining in Legislatures: An Experimental Investigation of Open versus Closed Amendment Rules," American Political Science Review, Cambridge University Press, vol. 97(2), pages 221-232, May.
    17. Breitmoser, Yves & Tan, Jonathan H.W., 2010. "Generosity in bargaining: Fair or fear?," MPRA Paper 27444, University Library of Munich, Germany.
    18. 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.
    19. Norman, Peter, 2002. "Legislative Bargaining and Coalition Formation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 322-353, February.
    20. 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.
    21. 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.
    22. Frechette, Guillaume & Kagel, John H. & Morelli, Massimo, 2005. "Nominal bargaining power, selection protocol, and discounting in legislative bargaining," Journal of Public Economics, Elsevier, vol. 89(8), pages 1497-1517, August.
    23. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    24. Harrington, Joseph E, Jr, 1990. "The Power of the Proposal Maker in a Model of Endogenous Agenda Formation," Public Choice, Springer, vol. 64(1), pages 1-20, January.
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    Cited by:

    1. Andrzej Baranski & Caleb A. Cox, 2023. "Communication in multilateral bargaining with joint production," Experimental Economics, Springer;Economic Science Association, vol. 26(1), pages 55-77, March.
    2. repec:nad:wpaper:20220080 is not listed on IDEAS
    3. Bradfield, Anthony J. & Kagel, John H., 2015. "Legislative bargaining with teams," Games and Economic Behavior, Elsevier, vol. 93(C), pages 117-127.
    4. Beviá, Carmen & Corchón, Luis C. & Yasuda, Yosuke, 2024. "Folk theorem under bankruptcy," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    5. Duozhe Li, 2014. "Multiplicity of Equilibrium Payoffs in Three-Player Baron-Ferejohn Model," Economics Bulletin, AccessEcon, vol. 34(2), pages 1122-1132.
    6. Berry, Kevin & Delmond, Anthony R. & Morin Chassé, Rémi & Strandholm, John C. & Shogren, Jason F., 2022. "A bargaining experiment under weak property rights, with implications for indigenous title claims," Ecological Economics, Elsevier, vol. 198(C).
    7. Andrzej Baranski & Caleb A. Cox, 2019. "Communication in Multilateral Bargaining with Joint Production," Working Papers 20190032, New York University Abu Dhabi, Department of Social Science, revised Nov 2019.
    8. Baranski, Andrzej & Haas, Nicholas, 2023. "The timing of communication and retaliation in bargaining: An experimental study," Journal of Economic Psychology, Elsevier, vol. 96(C).

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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