The Structure of Unstable Power Systems

Joseph M. Abdou (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics

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.

Mots clés: Interaction Form; Effectivity Function; Stability Index; Nash Equilibrium; Strong Equilibrium; Solvability; Acyclicity; Nakamura Number; Collusion

Mots clés: Indice de stabilité; Equilibre de Nash; Résolubilité; Acyclicité

Domaines: Economies et finances; Science politique

Joseph M. Abdou. The Structure of Unstable Power Systems. 2009. ⟨halshs-00389181⟩