The problem of multi-user commitment is one in which multiple users first commit to individual messages with a bookmaker and later reveal their messages. The objective of the bookmaker is then to decide whether the revealed messages correspond to the committed messages. We study a specific multi-user commitment model in which the users and the bookmaker have access to a noiseless channel, as well as a noisy multiple-access channel whose inputs are controlled by the users and whose output is observed by the bookmaker. When the users are non-colluding and the channel is non-redundant, we fully characterize the commitment capacity region. When the users are colluding, we derive an achievable region and a tight converse for the sum-rate. In both cases our proposed achievable commitment schemes are constructive.