It is widely assumed that aggressive behavior affects space acquisition in territorial species, but to date most workers have focused on competition for indivisible space, that is, space that cannot be divided or shared. We present a learning-based model that investigates the effects of aggressive interactions on space acquisition when unequal competitors arrive and settle in patches of divisible space. This model assumes that aggressive interactions act as punishment, in the sense that previous aggressive interactions in a given area reduce an individual's likelihood of returning to that area. Individually based, spatially explicit simulations incorporating this and other assumptions were used to investigate the effects of different types of aggressive interactions on the space use of individuals and dyads settling in divisible space. At the individual level, final space use was related to the amount of punishment that individuals inflicted on their opponents during aggressive interactions; in general, highly aggressive individuals acquired larger, more exclusive home ranges than less aggressive individuals. At the dyadic level, the division or sharing of space between competitors depended on both the relative and absolute punishment that competitors inflicted on one another during aggressive interactions. Aggressive interactions in which both participants strongly punished one another (e.g., escalated fights) produced mutually exclusive home ranges, interactions with intermediate levels of punishment produced asymmetrical space use patterns proportional to asymmetries in punishment levels, and interactions involving little punishment for either participant generated large home ranges with extensive home range overlap. Overall, our model implies that territorial animals need not "win" aggressive interactions to win divisible space, that repeatedly "nagging" an opponent may also be a viable strategy for gaining space, and that a learning-based approach can account for puzzling patterns in the territorial literature, for example, observations of individuals who acquire space by initiating aggressive interactions that they never win.