This paper presents a computational study of the effect of polydispersity in grafted polymers on the effective interactions between polymer grafted nanoparticles in a polymer matrix, when graft and matrix polymers are chemically identical. The potential of mean force (PMF) between grafted particles, calculated using a self-consistent PRISM theory-Monte Carlo simulation approach, shows that graft polydispersity weakens the attractive well at intermediate inter-particle distances, eliminating the well completely at high polydispersity index (PDI). The elimination of the mid-range attractive well is due to the longer grafts in the polydisperse distribution that introduce steric repulsion at large distances, and the increased wetting of the grafted layer by matrix chains arising from reduced monomer crowding within the polydisperse grafted layer. Trends in how the PMF changes as a function of grafting density, ratio of matrix to graft length, and packing fraction of polymer matrix seen for monodisperse grafts are preserved for polydisperse grafts. Comparison of a log-normal distribution to a bidisperse distribution of chain lengths (with equal number of short and long chains) with the same PDI and average length, shows that the polydisperse distribution can better stabilize dispersions than the bidisperse distributions because of the longer chains in the polydisperse distribution. Additionally, in a bidisperse distribution, with all chains shorter than the matrix chain length, there is a reduction in the mid-range attraction, thus confirming the role of reduced monomer crowding in the bidisperse grafted layer in increasing the grafted layer wetting by the matrix chains, and, as a result, improving miscibility of grafted particles and matrix.