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Sziklai Balázs (MTA KRTK):Axiomatic Cake Cutting
Abstract:
Cake Cutting refers to the classical fair division problem of dividing a heterogeneous resource among agents with different preferences. The literature splits into two parts: Computer scientists focus on how to compute solutions efficiently, while social choice theorists analyze the problem from axiomatic point of view. This presentation follows the latter path.
Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share) or all are worse-off (if there is less to share). We formally introduce these concepts to the cake-cutting problem and examine whether they are satisfied by various common division rules.
We prove that the Nash-optimal rule, which maximizes the product of utilities, is resource-monotonic and population-monotonic, in addition to being Pareto-optimal, envy-free and satisfying a strong competitive-equilibrium condition.