The coverage-dependent self-organization of Ce-adatoms on a Ag(111) surface is studied by scanning tunnelling microscopy at temperatures ranging from 3.9 to 10 K. At a coverage of 0.03% of a Ce monolayer individual Ce-adatoms and Ce dimers are observed, the mutual interatomic distances of which are clearly related to multiples of the Fermi wavelength λ_F/2, reflecting surface-state-mediated electronic interactions. At a coverage of 0.2% the formation of chains and small islands with hexagonal structure prevails. At a coverage of 1% a hexagonal superlattice with a periodicity of 3.2 nm is observed. At a coverage of 2% the superlattice of Ce-adatoms is found to be compressed, showing an interatomic distance of 2.2 nm. At higher coverage the number of dimers increases considerably and the superlattice collapses into compact islands. An increase in the temperature towards about 10 K at a coverage of 1% also causes the collapse of the hexagonal Ce superlattice. These experimental findings are rationalized within the electron scattering model of Hyldgard and Persson, which specifically takes into account the electronic surface-state on Ag(111). The experimentally derived two-body interaction potential is able to account for the observed phenomena as a function of concentration and temperature.