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The structure of unstable power mechanisms

Author

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  • Joseph M. Abdou

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We study the structure of unstable power mechanisms. A power mechanism is modeled by an interaction form, the solution of which is called a settlement. By stability, we mean the existence of some settlement for any preference profile. Configurations that produce instability are called cycles. We introduce a stability index that measures the difficulty of emergence of cycles. Structural properties such as exactness, superadditivity, subadditivity and maximality provide indications about the type of instability that may affect the mechanism. We apply our analysis to strategic game forms in the context of Nash-like solutions or core-like solutions. In particular, we establish an upper bound on the stability index of maximal interaction forms.

Suggested Citation

  • Joseph M. Abdou, 2012. "The structure of unstable power mechanisms," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00762018, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00762018
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    References listed on IDEAS

    as
    1. Stefano Vannucci, 2002. "Effectivity Functions and Stable Governance Structures," Annals of Operations Research, Springer, vol. 109(1), pages 99-127, January.
    2. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    3. Boros, Endre & Gurvich, Vladimir, 2000. "Stable effectivity functions and perfect graphs," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 175-194, March.
    4. J. Abdou, 1998. "Rectangularity and Tightness: A Normal Form Characterization of Perfect Information Extensive Game Forms," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 553-567, August.
    5. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151, Elsevier.
    6. Stefano Vannucci, 2008. "A coalitional game-theoretic model of stable government forms with umpires," Review of Economic Design, Springer;Society for Economic Design, vol. 12(1), pages 33-44, April.
    7. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
    8. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 345-356.
    9. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 187-204.
    10. Koji Takamiya & Akira Tanaka, 2006. "Computational Complexity in the Design of Voting Rules," ISER Discussion Paper 0653, Institute of Social and Economic Research, Osaka University, revised Jul 2006.
    11. Donald Campbell & Jerry Kelly, 2009. "Gains from manipulating social choice rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 349-371, September.
    12. Peleg, Bezalel, 2004. "Representation of effectivity functions by acceptable game forms: a complete characterization," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 275-287, May.
    13. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
    14. Mizutani, Masayoshi & Hiraide, Yasuhiko & Nishino, Hisakazu, 1993. "Computational Complexity to Verify the Unstability of Effectivity Function," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 225-239.
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    Cited by:

    1. Joseph Abdou, 2012. "Stability and index of the meet game on a lattice," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 775-789, November.
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    More about this item

    Keywords

    Interaction form; Effectivity function; Stability index; Nash equilibrium; Strong equilibrium; Solvability; Acyclicity; Nakamura number; Collusion;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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