We propose an online form of the cake cutting problem. This models situations where players 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 desirable properties that online cake cutting procedures might possess like online forms of proportionality and envy-freeness, and identify which properties are in fact possessed by the different online cake procedures.
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