We use molecular dynamics simulations to investigate the cooperative hydrodynamic interactions involved in the collective translation of a periodic array of spheres in a fluid which is confined between two atomistic surfaces. In particular, we study a spherical particle that is moving with a constant velocity parallel to the two confining surfaces. This central sphere along with its periodic images forms the translating two dimensional periodic grid. The cooperative hydrodynamic effects between neighboring spheres in the grid are determined by monitoring the friction force experienced by the spheres that are moving through an atomistic solvent. The dependence of the hydrodynamic cooperativity on the grid spacing is quantified by running simulations in systems with different sizes of the periodic box. Our results show a clear evidence of hydrodynamic cooperation between the spherical particles for grid spacing of 90 and larger, where is the solvent molecular diameter. These cooperative interactions lead to a reduced value of the friction force experienced by these spheres as opposed to the case for a single sphere moving in an infinite quiescent fluid. The simulated friction force values are compared with the recent continuum mechanics predictions [Bhattacharya, J. Chem. Phys. 128, 074709 (2008)] for the same problem of the motion of a periodic grid of particles through a confined fluid. The simulated values of friction force were found to follow the same qualitative trend as the continuum results but the continuum predictions were consistently larger than the simulation results by approximately 22%. We attribute this difference to the fluid slip at the surface of the spherical particle, as measured in the simulations.