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The Structure of Unstable Power Systems

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Author Info
Joseph Abdou () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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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, 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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00389181_v1.

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Date of creation: 13 May 2009
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Handle: RePEc:hal:cesptp:halshs-00389181_v1

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Related research
Keywords: Interaction Form; Effectivity Function; Stability Index; Nash Equilibrium; Strong Equilibrium; Solvability; Acyclicity; Nakamura Number; Collusion;

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  1. Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423 Elsevier. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August. [Downloadable!] (restricted)
  4. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June. [Downloadable!] (restricted)
  5. Joseph Abdou, 2009. "A Stability Index for Local Effectivity Functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00392508_v1, HAL. [Downloadable!]
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  6. 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. [Downloadable!] (restricted)
  7. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80. [Downloadable!] (restricted)
  8. Stefano Vannucci, 2008. "A coalitional game-theoretic model of stable government forms with umpires," Review of Economic Design, Springer, vol. 12(1), pages 33-44, April. [Downloadable!] (restricted)
  9. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  10. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May. [Downloadable!] (restricted)
  11. Peleg, Bezalel & Peters, Hans, 2009. "Nash consistent representation of effectivity functions through lottery models," Games and Economic Behavior, Elsevier, vol. 65(2), pages 503-515, March. [Downloadable!] (restricted)
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