This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to solve variational inequalities, we develop the algorithm converging to Nash equilibria in games, where players have no access to the full information but are able to communicate with neighbors over some communication graph. The convergence rate is demonstrated to be geometric and improves the rates obtained by the previously presented procedures seeking Nash equilibria in the class of games under consideration.