  Competitive equilibrium with equal incomes (CEEI) is a well known fair
allocation mechanism; however, for indivisible resources a CEEI may not exist.
It was shown in [Budish '11] that in the case of indivisible resources there is
always an allocation, called A-CEEI, that is approximately fair, approximately
truthful, and approximately efficient, for some favorable approximation
parameters. This approximation is used in practice to assign students to
classes. In this paper we show that finding the A-CEEI allocation guaranteed to
exist by Budish's theorem is PPAD-complete. We further show that finding an
approximate equilibrium with better approximation guarantees is even harder:
NP-complete.
