  Until now, the generation of an excitonic reservoir in a cavity polariton
system under quasi-resonant pumping has always been neglected. We show that in
microcavities having a small Rabi splitting (typically GaAs cavities with a
single quantum well), this reservoir can be efficiently populated by
polariton-phonon scattering. We consider the influence of the exciton reservoir
on the energy shifts of the resonantly pumped polariton modes. We show that the
presence of this reservoir effectively reduces the spin anisotropy of the
polariton-polariton interaction, in agreement with recent experimental
measurements, where the multistability of cavity polaritons has been analyzed
