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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
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    File URL: https://www.nottingham.ac.uk/cedex/documents/papers/cedex-discussion-paper-2012-04.pdf
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    References listed on IDEAS

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    1. repec:cup:apsrev:v:83:y:1989:i:04:p:1181-1206_08 is not listed on IDEAS
    2. Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
    3. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    4. Manfred J. Holler & Stefan Napel, 2004. "Monotonicity of power and power measures," Theory and Decision, Springer, vol. 56(2_2), pages 93-111, February.
    5. 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.
    6. repec:cup:apsrev:v:93:y:1999:i:04:p:809-820_21 is not listed on IDEAS
    7. repec:cup:apsrev:v:101:y:2007:i:04:p:847-850_07 is not listed on IDEAS
    8. Montero, Maria & Vidal-Puga, Juan J., 2007. "Demand Commitment in Legislative Bargaining," American Political Science Review, Cambridge University Press, vol. 101(04), pages 847-850, November.
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    Keywords

    monotonicity; noncoopeative;

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