  Reduced density-matrix functional theory (RDMFT) has become an appealing
alternative to density-functional theory to describe electronic properties of
highly-correlated systems. Here we derive exact conditions for the suitability
of RDMFT to describe the two-dimensional homogeneous electron gas, which is the
base system for, e.g., semiconductor quantum dots and quantum Hall devices.
Following the method of Cioslowski and Pernal [J. Chem. Phys. {\bf 111}, 3396
(1999)] we focus on the properties of power functionals of the form $f(n,n')=(n
n')^\alpha$ for the scaling function in the exchange-correlation energy. We
show that in order to have stable and analytic solutions, and for $f$ to
satisfy the homogeneous scaling constraint, the power is restricted to $1/4
\leq \alpha \leq 3/4$. Applying a reasonable ansatz for the momentum
distribution and the lower bound for the exchange-correlation energy tightens
the physical regime further to $0.64 \lesssim \alpha \leq 0.75$.
