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The Structure of Unstable Power Systems

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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 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 Abdou, 2009. "The Structure of Unstable Power Systems," Documents de travail du Centre d'Economie de la Sorbonne 09042, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:09042
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    Keywords

    Interaction form; effectivity function; stability index; Nash equilibrium; strong equilibrium; solvability; acyclicity; Nakamura number; collusion;

    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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