Simultaneous Cake Cutting

We introduce the simultaneous model for cake cutting (the fair allocation of a divisible good), in which agents simul-taneously send messages containing a sketch of their pref-erences over the cake. We show that this model enables the computation of divisions that satisfy proportionality — a popular fairness notion — using a protocol that circumvents a standard lower bound via parallel information elicitation. Cake divisions satisfying another prominent fairness notion, envy-freeness, are impossible to compute in the simultaneous model, but such allocations admit arbitrarily good approxi-mations