# The Structure of Unstable Power Systems

Working paper

Issue number:

2009.42

Publisher:

Centre dâ€™Economie de la Sorbonne

Year:

2009

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 proper-ties 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.