Equitable Cake Cutting without Mediator

We consider enhancing solutions to the fair division problem of cake cutting by proposing a cryptographic protocol preserving the privacy of the players’ preferences in each step. This addresses an important shortcoming of traditional division procedures, that disclose some of the players’ preferences and offer other players the possibility to dynamically adjust their behaviour in order to obtain unfair advantages. By contrast, the only thing that players learn when applying our procedure is strictly minimal, that is, players only learn the cutting point that would be determined by a fair mediator. Our approach relies on the description of the players’ utility function through step functions, a choice that enables us to obtain an efficient procedure for the secure evaluation of cutting points in the two-player case. We also explore a procedure that could be applied for more players.