In this paper we consider the Italian banking industry, where the eight largest firms operate at a national level, manage about a half of total loans, and have a notably larger dimension than the other competitors. We estimate a structural model containing a behavioural parameter, in order to assess the market conduct of the largest banks for the period 1988-2000. Our finding is that, in spite of their noteworthy size and significant market share, these banks have been characterised by a more competitive conduct than the Bertrand-Nash outcome: this is in line with the results of the latest literature of the field, for which in the banking industry there is often no conflict between competition and concentration.