IDEAS home Printed from https://ideas.repec.org/p/not/notcdx/2012-04.html
   My bibliography  Save this paper

A Violation of Monotonicity in a Noncooperative Setting

Author

Listed:
  • Maria Montero

    (School of Economics, University of Nottingham)

  • Juan Vidal-Puga

    (Faculty of Economics and Management, Universidade de Vigo)

Abstract

A power measure is monotone if a player with a larger weight is assigned at least as much power as a player with a smaller weight in the same weighted majority game. Failure of a power index to satisfy monotonicity is often considered a pathological feature. In this paper, we show that monotonicity may fail in the unique subgame perfect equilibrium of a noncooperative bargaining game. A player with a smaller weight may have a higher expected payoff than a player with a larger weight. This is possible even though coalition formation and payoff division are endogenous, all players are rational and there is no asymmetry between the players other than in the weights.

Suggested Citation

  • Maria Montero & Juan Vidal-Puga, 2012. "A Violation of Monotonicity in a Noncooperative Setting," Discussion Papers 2012-04, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    • Handle: RePEc:not:notcdx:2012-04
    as

    Download full text from publisher

    File URL: https://www.nottingham.ac.uk/cedex/documents/papers/cedex-discussion-paper-2012-04.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    2. 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.
    3. Bennett, E. & van Damme, E.E.C., 1990. "Demand commitment bargaining : The case of apex games," Discussion Paper 1990-62, Tilburg University, Center for Economic Research.
    4. Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
    5. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    7. Manfred J. Holler & Stefan Napel, 2004. "Monotonicity of power and power measures," Theory and Decision, Springer, vol. 56(2_2), pages 93-111, February.
    8. 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.
    9. Morelli, Massimo, 1999. "Demand Competition and Policy Compromise in Legislative Bargaining," American Political Science Review, Cambridge University Press, vol. 93(4), pages 809-820, December.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    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. Breitmoser, Yves & Tan, Jonathan H.W., 2011. "Ultimata bargaining: generosity without social motives," MPRA Paper 33613, University Library of Munich, Germany.
    2. Breitmoser, Yves & Tan, Jonathan H.W., 2013. "Reference dependent altruism in demand bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 127-140.
    3. 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.
    4. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2023. "An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value," Games and Economic Behavior, Elsevier, vol. 141(C), pages 88-104.
    5. 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.
    6. Chen, Ying & Eraslan, Hülya, 2013. "Rhetoric in legislative bargaining with asymmetric information," Discussion Paper Series In Economics And Econometrics 1309, Economics Division, School of Social Sciences, University of Southampton.
    7. Yves Breitmoser, 2009. "Demand commitments in majority bargaining or how formateurs get their way," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 183-191, June.
    8. 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.
    9. Michela Chessa & Nobuyuki Hanaki & Aymeric Lardon & Takashi Yamada, 2021. "An Experiment on the Nash Program: Comparing two Mechanisms Implementing the Shapley Value," GREDEG Working Papers 2021-07, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    10. Breitmoser, Yves, 2011. "Binomial menu auctions in government formation," MPRA Paper 28576, University Library of Munich, Germany.
    11. Gantner, Anita & Horn, Kristian & Kerschbamer, Rudolf, 2016. "Fair and efficient division through unanimity bargaining when claims are subjective," Journal of Economic Psychology, Elsevier, vol. 57(C), pages 56-73.
    12. Aaron Kamm & Simon Siegenthaler, 2024. "Commitment timing in coalitional bargaining," Experimental Economics, Springer;Economic Science Association, vol. 27(1), pages 130-154, March.
    13. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    14. , & ,, 2014. "Rhetoric in legislative bargaining with asymmetric information," Theoretical Economics, Econometric Society, vol. 9(2), May.
    15. Eric Guerci & Nobuyuki Hanaki & Naoki Watanabe & Gabriele Esposito & Xiaoyan Lu, 2014. "A methodological note on a weighted voting experiment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 827-850, December.
    16. Marco Battaglini & Stephen Coate, 2008. "A Dynamic Theory of Public Spending, Taxation, and Debt," American Economic Review, American Economic Association, vol. 98(1), pages 201-236, March.
    17. Hsu, Li-Chen & Yang, C.C. & Yang, Chun-Lei, 2008. "Positive- versus zero-sum majoritarian ultimatum games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 68(3-4), pages 498-510, December.
    18. Maaser, Nicola & Paetzel, Fabian & Traub, Stefan, 2019. "Power illusion in coalitional bargaining: An experimental analysis," Games and Economic Behavior, Elsevier, vol. 117(C), pages 433-450.
    19. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, vol. 6(2), pages 1-18, April.
    20. Anita Gantner & Kristian Horn & Rudolf Kerschbamer, 2013. "Fair Division in Unanimity Bargaining with Subjective Claims," Working Papers 2013-31, Faculty of Economics and Statistics, Universität Innsbruck.

    More about this item

    Keywords

    monotonicity; noncoopeative;

    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:not:notcdx:2012-04. 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: Jose V Guinot Saporta (email available below). General contact details of provider: https://edirc.repec.org/data/cdnotuk.html .

    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.