IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v6y2015i2p39-56d48616.html
   My bibliography  Save this article

A Model of Protocoalition Bargaining with Breakdown Probability

Author

Listed:
  • Maria Montero

    (School of Economics, University of Nottingham, University Park, NG7 2RD Nottingham, UK)

Abstract

This paper analyses a model of legislative bargaining in which parties form tentative coalitions (protocoalitions) before deciding on the allocation of a resource. Protocoalitions may fail to reach an agreement, in which case they may be dissolved (breakdown) and a new protocoalition may form. We show that agreement is immediate in equilibrium, and the proposer advantage disappears as the breakdown probability goes to zero. We then turn to the special case of apex games and explore the consequences of varying the probabilities that govern the selection of formateurs and proposers. Letting the breakdown probability go to zero, most of the probabilities considered lead to the same ex post pay-off division. Ex ante expected pay-offs may follow a counterintuitive pattern: as the bargaining power of weak players within a protocoalition increases, the weak players may expect a lower pay-off ex ante.

Suggested Citation

  • Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, vol. 6(2), pages 1-18, April.
    • Handle: RePEc:gam:jgames:v:6:y:2015:i:2:p:39-56:d:48616
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/6/2/39/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/6/2/39/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    2. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    3. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    4. Tasos Kalandrakis, 2006. "Proposal Rights and Political Power," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 441-448, April.
    5. 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..
    6. Tomohiko Kawamori, 2005. "Players' Patience and Equilibrium Payoffs in the Baron-Ferejohn Model," Economics Bulletin, AccessEcon, vol. 3(43), pages 1-5.
    7. Michael Laver & Scott Marchi & Hande Mutlu, 2011. "Negotiation in legislatures over government formation," Public Choice, Springer, vol. 147(3), pages 285-304, June.
    8. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    9. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    10. Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
    11. David P. Baron & Daniel Diermeier, 2001. "Elections, Governments, and Parliaments in Proportional Representation Systems," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(3), pages 933-967.
    12. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    13. Diermeier, Daniel & Merlo, Antonio, 2000. "Government Turnover in Parliamentary Democracies," Journal of Economic Theory, Elsevier, vol. 94(1), pages 46-79, September.
    14. Karos, Dominik, 2014. "Coalition formation in general apex games under monotonic power indices," Games and Economic Behavior, Elsevier, vol. 87(C), pages 239-252.
    15. 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.
    16. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Jackson, Matthew O. & Moselle, Boaz, 2002. "Coalition and Party Formation in a Legislative Voting Game," Journal of Economic Theory, Elsevier, vol. 103(1), pages 49-87, March.
    18. Jon X. Eguia, 2011. "Endogenous Parties in an Assembly," American Journal of Political Science, John Wiley & Sons, vol. 55(1), pages 16-26, January.
    19. Guillaume Fréchette & John H. Kagel & Massimo Morelli, 2005. "Behavioral Identification in Coalitional Bargaining: An Experimental Analysis of Demand Bargaining and Alternating Offers," Econometrica, Econometric Society, vol. 73(6), pages 1893-1937, November.
    20. Daniel Diermeier & Hulya Eraslan & Antonio Merlo, 2003. "A Structural Model of Government Formation," Econometrica, Econometric Society, vol. 71(1), pages 27-70, January.
    21. 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.
    22. Diermeier, Daniel & Merlo, Antonio, 2004. "An empirical investigation of coalitional bargaining procedures," Journal of Public Economics, Elsevier, vol. 88(3-4), pages 783-797, March.
    23. 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.
    24. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    25. Yves Breitmoser, 2012. "Proto-coalition bargaining and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 581-599, November.
    26. Daniel Seidmann & Eyal Winter & Elan Pavlov, 2007. "The Formateurs’ Role in Government Formation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 427-445, June.
    27. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
    28. Browne, Eric C. & Franklin, Mark N., 1973. "Aspects of Coalition Payoffs in European Parliamentary Democracies," American Political Science Review, Cambridge University Press, vol. 67(2), pages 453-469, June.
    29. 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.
    30. McKelvey, Richard D. & Ordeshook, Peter C. & Winer, Mark D., 1978. "The Competitive Solution for N-Person Games Without Transferable Utility, With an Application to Committee Games," American Political Science Review, Cambridge University Press, vol. 72(2), pages 599-615, June.
    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. Maria Montero, 2023. "Coalition Formation in Games with Externalities," Dynamic Games and Applications, Springer, vol. 13(2), pages 525-548, June.
    2. Gomes, Armando, 2022. "Coalitional bargaining games: A new concept of value and coalition formation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 463-477.
    3. Kawamori, Tomohiko, 2022. "Coalition-then-allocation legislative bargaining," Journal of Mathematical Economics, Elsevier, vol. 99(C).

    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. Gomes, Armando, 2022. "Coalitional bargaining games: A new concept of value and coalition formation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 463-477.
    3. 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.
    4. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Kalandrakis, Tasos, 2015. "Computation of equilibrium values in the Baron and Ferejohn bargaining model," Games and Economic Behavior, Elsevier, vol. 94(C), pages 29-38.
    10. Maria Montero, 2023. "Coalition Formation in Games with Externalities," Dynamic Games and Applications, Springer, vol. 13(2), pages 525-548, June.
    11. Montero, Maria & Vidal-Puga, Juan J., 2007. "Demand Commitment in Legislative Bargaining," American Political Science Review, Cambridge University Press, vol. 101(4), pages 847-850, November.
    12. Breitmoser, Yves & Tan, Jonathan H.W., 2014. "Reference Dependent Altruism," MPRA Paper 52774, University Library of Munich, Germany.
    13. Montero, Maria & Vidal-Puga, Juan J., 2011. "Demand bargaining and proportional payoffs in majority games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 395-408, March.
    14. Evdokimov, Kirill S., 2023. "Equality in legislative bargaining," Journal of Economic Theory, Elsevier, vol. 212(C).
    15. Antonio Merlo, 2005. "Whither Political Economy? Theories, Facts and Issues," PIER Working Paper Archive 05-033, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2005.
    16. Maria Montero, 2023. "Bargaining in Legislatures: A New Donation Paradox," Studies in Choice and Welfare, in: Sascha Kurz & Nicola Maaser & Alexander Mayer (ed.), Advances in Collective Decision Making, pages 159-171, Springer.
    17. Yves Breitmoser, 2012. "Proto-coalition bargaining and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 581-599, November.
    18. Hughes, Niall, 2016. "Voting in legislative elections under plurality rule," Journal of Economic Theory, Elsevier, vol. 166(C), pages 51-93.
    19. David P Baron, 2018. "Elections and durable governments in parliamentary governments," Journal of Theoretical Politics, , vol. 30(1), pages 74-118, January.
    20. Maria Montero, 2010. "Bargaining in Legislatures: A New Donation Paradox," Discussion Papers 2010-19, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.

    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:gam:jgames:v:6:y:2015:i:2:p:39-56:d:48616. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.