This paper shows an avenue through which a numerical inflation target ensures low inflation and high credibility; one that is independent of the usual Walsh incentive contract. Our novel game theoretic framework - a generalization of alternating move games - formalizes the fact that since the target is explicit/legislated, it cannot be frequently reconsidered. This ‘explicitness’ therefore serves as a commitment device. There are two key results. First, it is shown that if the inflation target is sufficiently rigid (explicit) relative to the public’s wages, low inflation is time consistent and hence credible even if the policymaker’s output target is above potential. Second, it is found that the central banker’s optimal explicitness level is decreasing in the degree of her patience/independence (due to their substitutability in achieving credibility). Our analysis therefore offers an explanation for the ‘inflation and credibility convergence’ over the past two decades as well as the fact that inflation targets were legislated primarily by countries that had lacked central bank independence like New Zealand, Canada, and the UK rather than the US, Germany, or Switzerland. We show that there exists fair empirical support for all the predictions of our analysis.