Equilibria of Generalized Cut and Choose Protocols

Classic cake cutting protocols — which fairly allocate a divisible good among agents with heterogeneous preferences — are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? We model the interaction among agents as a game and study its Nash equilibria. We show that each protocol in the novel class of generalized cut and choose protocols — which includes the most important discrete cake cutting protocols — is guaranteed to have an ε-equilibrium for all ε > 0. Moreover, we observe that the (approximate) equilibria of proportional protocols — which guarantee each of the n agents a 1/n-fraction of the cake — must be (approximately) proportional. Finally, we design a generalized cut and choose protocol where all equilibrium outcomes satisfy the stronger fairness notion of envy-freeness.