  The classic cake cutting problem concerns the fair allocation of a
heterogeneous resource among interested agents. In this paper, we study a
public goods variant of the problem, where instead of competing with one
another for the cake, the agents all share the same subset of the cake which
must be chosen subject to a length constraint. We focus on the design of
truthful and fair mechanisms in the presence of strategic agents who have
piecewise uniform utilities over the cake. On the one hand, we show that the
leximin solution is truthful and moreover maximizes an egalitarian welfare
measure among all truthful and position oblivious mechanisms. On the other
hand, we demonstrate that the maximum Nash welfare solution is truthful for two
agents but not in general. Our results assume that mechanisms can block each
agent from accessing parts that the agent does not claim to desire; we provide
an impossibility result when blocking is not allowed.
