The Structure of Unstable Power Systems
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.
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