The paper examines whether central banks should be committed to achieving price stability (a low-inflation target), and how strong (explicit) their long-term monetary commitment should be. For that purpose we propose a game theoretic framework that enables us to model various degrees of commitment, as well as its endogenous determination. Our main policy contribution consists in showing that the socially optimal degree of long-term monetary commitment depends on: (i) the potential short-term cost in terms of reduced stabilization flexibility, (ii) the potential benefit in terms of better anchored expectations, (iii) the structure of the economy, (iv) agents’expectations formation, and (v) the degrees of the central bank’s conservatism (strictness) and ambition. The latter point implies substitutability between explicit inflation targeting and central bank goal-independence, and offers a possible explanation for the fact that countries with originally low degrees of central bank goal-independence have tended to commit more explicitly to price stability (legislate a unitary or hierarchical mandate rather than a dual mandate).