Stability Index of Interaction forms
Résumé
An interaction form is an abstract model of interaction based on a
description of power distribution among agents over alternatives. A solution
known as the settlement set is defined at any preference profile. Necessary
and sufficient conditions for stability, that is the existence of settlements, are
established. A Stability Index that plays a role similar to that of the Naka-
mura Number is defined. It measures, loosely speaking, the complexity of
those configurations that prevent a settlement. To any strategic game form
one can associate an interaction form in such a way that given an equilibrium
concept (e.g. Nash or strong Nash) and a preference profile, settlements of
the interaction form are precisely the equilibrium outcomes of the resulting
game. As a consequence we have necessary and sufficient conditions for the
solvability of game forms. The paper provides a localization of the index in
case of unstability.
description of power distribution among agents over alternatives. A solution
known as the settlement set is defined at any preference profile. Necessary
and sufficient conditions for stability, that is the existence of settlements, are
established. A Stability Index that plays a role similar to that of the Naka-
mura Number is defined. It measures, loosely speaking, the complexity of
those configurations that prevent a settlement. To any strategic game form
one can associate an interaction form in such a way that given an equilibrium
concept (e.g. Nash or strong Nash) and a preference profile, settlements of
the interaction form are precisely the equilibrium outcomes of the resulting
game. As a consequence we have necessary and sufficient conditions for the
solvability of game forms. The paper provides a localization of the index in
case of unstability.
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