We report results of a theoretical investigation into the mutual annihilation of tight-binding excitons. The results are in apparent contradiction with intuitive expectations and provide corrections to expressions given by one of the present authors (V.M.K.) in an earlier analysis. A part of that analysis was based on a mapping of the dynamics of two mobile, mutually annihilating excitons onto the dynamics of a single exciton migrating in the presence of a fixed trap. We find that while this equivalence is valid for incoherent, randomly walking particles in an ordered system, it does not hold for an arbitrary degree of transport coherence. Any nonvanishing coherence makes a moving trap, i.e., a second exciton, less effective than the corresponding stationary trap. For realistic intersite interactions, the quantum yield for annihilation passes through a maximum, i.e., the fluorescence yield passes through a minimum, as the exciton motion becomes less coherent. The earlier predictions are recovered in the incoherent limit
