The aim of this work is to verify whether there is an inflation bias in the Euro-area monetary policy. I verify the presence of a strategic repeated game between the European Central Bank and the market, in setting actual and expected inflation, and consider the features of this game. In particular, the aim is to verify whether the market fixes the expected inflation strategically, and how the probability of the kind of monetary policy is formed. It can be concluded that the market behaves strategically, but an inflation bias does not emerge from data. The source of non-credibility cannot be the bank's lack of commitment, but it may be a partial inability to control or to communicate economic shocks. These conclusions are robust to two different estimation strategies, which are both based on regime-switching regressions. The effects of the recent financial and sovereign-debt crises are taken into account.