P-Stable Equilibrium : Definition and Some Properties

We define a continuous index of strategic stability,p.stability, which requires equilibrium to be the unique outcome compatible with common knowledge of rationality and common knowledge of p.beliefs (beliefs that put probability at least p on the equilibrium profile). We show that every equilibrium (within a large class) is p-stable for some p < 1 and justify, in smooth settings, the intuition that the slope of the best response map is related to the stability of equilibrium. We show that adding incomplete information on fundamentals could decrease the degree of strategic stability. In two applications to large markets we (i) show that a unique equilibrium globally unstable (under tâtonnement dynamics) has, nevertheless, a measure of strategic stability, (ii) characterize the conditions under which enhanced equilibrium efficiency results in decreased strategic stability.