Abstract The lateral interactions in silver submonolayers on W(110) are estimated by comparing phase diagrams calculated by means of Monte Carlo techniques with an experimental phase diagram inferred from work function and thermal desorption spectroscopy measurements. Pairwise interactions alone, at least within the ranges considered in this paper, do not seem to be able to reproduce part of the experimental phase diagram. The additional use of three-body interactions, however, introduces a desired asymmetry into the calculated phase diagrams, resulting in a reasonably close fit with the experimental phase diagram. Best-fit estimates for the lateral interactions were obtained by assuming attractive first-nearest-neighbour and repulsive second- and third-nearest-neighbour interactions, together with two different types of attractive three-body interaction. Ground state phase diagrams for adsorbates with pairwise interactions extending up to the fifth nearest neighbour and two different types of three-body interaction are discussed in detail for attractive first-nearest-neighbour interactions and b.c.c. (110) substrates.