Abstract
We study envy-free cake cutting with strategic
agents, where each agent may manipulate his private information in order to receive a better allocation. We focus on piecewise constant utility functions and consider two scenarios: the general setting without any restriction on the allocations and
the restricted setting where each agent has to receive a connected piece. We show that no deterministic truthful envy-free mechanism exists in the
connected piece scenario, and the same impossibility result for the general setting with some additional mild assumptions on the allocations. Finally,
we study a large market model where the economy
is replicated and demonstrate that truth-telling converges to a Nash equilibrium.