  We propose an online form of the cake cutting problem. This models situations
where agents arrive and depart during the process of dividing a resource. We
show that well known fair division procedures like cut-and-choose and the
Dubins-Spanier moving knife procedure can be adapted to apply to such online
problems. We propose some fairness properties that online cake cutting
procedures can possess like online forms of proportionality and envy-freeness.
We also consider the impact of collusion between agents. Finally, we study
theoretically and empirically the competitive ratio of these online cake
cutting procedures. Based on its resistance to collusion, and its good
performance in practice, our results favour the online version of the
cut-and-choose procedure over the online version of the moving knife procedure.
