  Observed kinematical data of 40 Local Group (LG) members are used to derive
the dark matter halo mass of such galaxies. Haloes are selected from the
theoretically expected LG mass function and two different density profiles are
assumed, a standard universal cuspy model and a mass dependent profile which
accounts for the effects of baryons in modifying the dark matter distribution
within galaxies. The resulting relations between stellar and halo mass are
compared with expectations from abundance matching.
  Using a universal cuspy profile, the ensemble of LG galaxies is fit in
relatively low mass haloes, leaving "dark" many massive haloes of
\mhalo$\gtrsim$10$^{10}$\msun: this reflects the "too big to fail" problem and
results in a \mstar-\mhalo\ relation that differs from abundance matching
predictions. Moreover, the star formation efficiency of isolated LG galaxies
increases with decreasing halo mass when adopting a cuspy model. By contrast,
using the mass dependent density profile, dwarf galaxies with
\mstar$\gtrsim$10$^{6}$\msun are assigned to more massive haloes, which have a
central cored distribution of dark matter: the "too big to fail" problem is
alleviated, the resultant \mstar-\mhalo\ relation follows abundance matching
predictions down to the completeness limit of current surveys, and the star
formation efficiency of isolated members decreases with decreasing halo mass,
in agreement with theoretical expectations.
  Finally, the cusp/core space of LG galaxies is presented, providing a
framework to understand the non-universality of their density profiles.
