A minimal central bank credibility, with a non-zero probability of not renegning his commitment ("quasi-commitment"), is a necessary condition for anchoring inflation expectations and stabilizing inflation dynamics. By contrast, a complete lack of credibility, with the certainty that the policy maker will renege his commitment ("optimal discretion"), leads to the local instability of inflation dynamics. In the textbook example of the new-Keynesian Phillips curve, the response of the policy instrument to inflation gaps for optimal policy under quasi-commitment has an opposite sign than in optimal discretion, which explains this bifurcation.