  Perturbative QCD predicts that the growth of the gluon density at high
energies should saturate, forming a Color Glass Condensate (CGC), which is
described in mean field approximation by the Balitsky-Kovchegov (BK) equation.
In this paper we study the $\gamma \gamma$ interactions at high energies and
estimate the main observables which will be probed at future linear colliders
using the color dipole picture. We discuss in detail the dipole - dipole cross
section and propose a new relation between this quantity and the dipole
scattering amplitude. The total $\gamma \gamma$, $\gamma^{*} \gamma^{*}$
cross-sections and the real photon structure function $F_2^{\gamma}(x,Q^2)$ are
calculated using the recent solution of the BK equation with running coupling
constant and the predictions are compared with those obtained using
phenomenological models for the dipole-dipole cross section and scattering
amplitude. We demonstrate that these models are able to describe the LEP data
at high energies, but predict a very different behavior for the observables at
higher energies. Therefore we conclude that the study of $\gamma \gamma$
interactions can be useful to constrain the QCD dynamics.
