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The Structure of Unstable Power Systems

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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

A power system 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. Like in other models of power structure, instability is equivalent to the existence of a cycle. Structural properties of the system like maximality, regularity, superadditivity, subadditivity and exactness are defined and used to determine the type of instability that may affect the system. A Stability Index is introduced. Loosely speaking this index measures the difficulty of the emergence of configurations that produce a deadlock. As applications we have a characterization of solvable game forms, an analysis of the structure of their instability and a localization of their stability index in case where solvability fails.

Suggested Citation

  • Joseph M. Abdou, 2009. "The Structure of Unstable Power Systems," Working Papers halshs-00389181, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00389181
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00389181
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    References listed on IDEAS

    as
    1. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    2. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    3. 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.
    4. 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.
    5. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
    6. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 187-204.
    7. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
    8. 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.
    9. Abdou, J., 1994. "Strongly consistent two-player game forms," Economics Letters, Elsevier, vol. 44(4), pages 377-380, April.
    10. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Interaction Form; Effectivity Function; Stability Index; Nash Equilibrium; Strong Equilibrium; Solvability; Acyclicity; Nakamura Number; Collusion; Indice de stabilité; Equilibre de Nash; Résolubilité; Acyclicité;
    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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