Abstract This paper concerns the exploitative competition of two predators for two prey species. We analyze the model proposed by MacArthur with more general parameters. MacArthur used the model to address questions of species packing on resources, but he did not completely determine analytically under what conditions will neither, one, or both predator species and one or both prey species, survive. Our analysis is global for all cases except one, for which we performed a numerical analysis. We conclude that the behavior of this predator-prey system is more complicated than previously thought. In particular, we analyze cases in which the two-predator, two-prey system catastrophically collapses to a one-predator, two-prey system, or even to one-predator, one-prey system. We also show that there are cases in which the initial numbers of the two predators determine the pattern of this collapse. These conclusions suggest that caution should be exercised in interpreting any conclusions of species packing that are based solely upon a graphical analysis of the MacArthur model.