Theoretical models for the expected merger rates of intermediate-mass black holes ( IMBHs ) are vital for planned gravitational-wave detection experiments such as the Laser Interferometer Space Antenna ( LISA ) . Using collisionless N -body simulations of dwarf galaxy ( DG ) mergers , we examine how the orbital decay of IMBHs and the efficiency of IMBH binary formation depend on the central dark matter ( DM ) density profile of the merging DGs . Specifically , we explore various asymptotic inner slopes \gamma of the DG ’ s DM density distribution , ranging from steep cusps ( \gamma = 1 ) to shallower density profiles ( \gamma < 1 ) , motivated by well-known baryonic-feedback effects as well as by DM models that differ from cold DM at the scales of DGs . We find that the inner DM slope is crucial for the formation ( or lack thereof ) of an IMBH binary ; only mergers between DGs with cuspy DM profiles ( \gamma = 1 ) are favourable to forming a hard IMBH binary , whereas when \gamma < 1 the IMBHs stall at a separation of 50–100 pc . Consequently , the rate of LISA signals from IMBH coalescence will be determined by the fraction of DGs with a cuspy DM profile . Conversely , the LISA event rates at IMBH mass scales offer in principle a novel way to place constraints on the inner structure of DM halos in DGs and address the core–cusp controversy . We also show that , with spatial resolutions of \sim 0.1 kpc , as often adopted in cosmological simulations , all IMBHs stall , independent of \gamma . This suggests caution in employing cosmological simulations of galaxy formation to study BH dynamics in DGs .