Godfray's influential model of competitive begging predicted that offspring should respond to each other's behavior, displaying more intensely when competing with needier rivals. Empirical tests of this prediction have, however, yielded equivocal results. Here, I develop a series of evolutionarily stable strategy models of begging as a signal of need, which show that this prediction holds only for competitive aspects of display that influence the division of food among the brood. No such response is expected for cooperative begging (which influences the total level of provisioning by the parent), and the models even predict the opposite trend under some circumstances (where the indirect costs of extracting additional resources from the parent are high). These contrasting sets of predictions may help to explain the varying empirical results obtained by studies of sibling interaction. Cooperative (as opposed to competitive) begging is likely to be of greater significance in cases where dominant young can gain direct control of allocation (or enjoy some competitive advantage). Dominants are then predicted to parasitize the efforts of their weaker rivals and reduce their own investment in cooperative signaling while continuing to claim a disproportionately large share of the resources provided by the parent.