Using density-functional theory with the local-density approximation and the generalized gradient approximation we compute the energy barriers for surface diffusion for Ag on Pt (111), Ag on one monolayer of Ag on Pt (111), and Ag on Ag (111). The diffusion barrier for Ag on Ag (111) is found to increase linearly with increasing lattice constant. We also discuss the reconstruction that has been found experimentally when two Ag layers are deposited on Pt (111). Our calculations explain why this strain driven reconstruction occurs only after two Ag layers have been deposited.