The interaction between quantum well excitons and cavity photons in semiconductor microcavities in the strong coupling regime results in mixed $\mathrm{2D}$ exciton — photon states, called exciton polaritons. The behavior of a dense polariton system is of particular interest due to the fact that these particles have integer spin and, hence, obey Bose–Einstein statistics. Drastic nonlinearities have been observed both in the low polariton (LP) emission intensity and polarization in the case of the resonant excitation into the LP branch under condition that $2\hbar\omega(k_{\mathrm{ex}})=\hbar\omega(k=0)+\hbar\omega(2k_{\mathrm{ex}})$. The experiments have shown a very strong final state stimulation of a two polariton scattering due to the bosonic nature of the polaritons. The filling of $k=0$ LP state significantly exceeding $1$ has been realized under continuous excitation at $T=1.8$ K. The dependence of the effect on the polarization of photoexcited light and temperature is discussed.