The structure of unstable power mechanisms

Joseph M. Abdou (1, 2)

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

We study the structure of unstable power mechanisms. A power mechanism 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. Configurations that produce instability are called cycles. We introduce a stability index that measures the difficulty of emergence of cycles. Structural properties such as exactness, superadditivity, subadditivity and maximality provide indications about the type of instability that may affect the mechanism. We apply our analysis to strategic game forms in the context of Nash-like solutions or core-like solutions. In particular, we establish an upper bound on the stability index of maximal interaction forms.

Mots clés: Interaction form; Effectivity function; Stability index; Nash equilibrium; Strong equilibrium; Solvability; Acyclicity; Nakamura number; Collusion

Domaines: Economies et finances

Joseph M. Abdou. The structure of unstable power mechanisms. Economic Theory, 2012, 50, pp.389 - 415. ⟨halshs-00762018⟩