  Several groups of authors have analyzed Fermi LAT data in a region around the
Galactic Center finding an unaccounted gamma-ray excess over diffuse
backgrounds in the GeV energy range. It has been argued that it is difficult or
even impossible to explain this diffuse emission by the leading astrophysical
candidates - millisecond pulsars (MSPs). Here we provide a new estimate of the
contribution to the excess by a population of yet unresolved MSP located in the
bulge of the Milky Way. We simulate this population with the GALPLOT package by
adopting a parametric approach, with the range of free parameters gauged on the
MSP characteristics reported by the second pulsar catalogue (2PC). We find that
the conclusions strongly depend on the details of the MSP luminosity function
(in particular, its high luminosity end) and other explicit or tacit
assumptions on the MSP statistical properties, which we discuss. Notably, for
the first time we study the importance of the possible secondary emission of
the MSPs in the Galactic Center, {i.e. the emission via inverse Compton losses
of electrons injected in the interstellar medium. Differently from a majority
of other authors, we find that within current uncertainties a large if not
dominant contribution of MSPs to the excess cannot be excluded. We also show
that the sensitivities of future instruments or possibly already of the latest
LAT data analysis (Pass 8) provide good perspectives to test this scenario by
resolving a significant number of MSPs.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology