We present a novel molecular dynamics simulation technique, which accounts for both two- and three-body dispersion interactions. This technique is a unified approach of molecular dynamics and quantum mechanical variational methods, in the spirit of the Car - Parrinello method (1985 Phys. Rev. Lett. 55 2471). We use a highly simplified model for the electronic structure of the atoms, which is, nevertheless, sufficient to correctly reproduce the London two-body, and the Axilrod - Teller three-body dispersion forces in an appropriate limit. The advantage of this new method is that it allows for a consistent treatment of both dispersion damping and periodic boundary conditions at the pair and three-body levels.