Competition for limited resources can have fundamental implications for population dynamics. However, the effects of resource depletion have rarely been discussed in the context of sexual selection, even though mate choice typically favours males who outperform others in securing access to some limited resource. Here, we develop a model to investigate the question of resource competition as a form of male-male competition in the context of male sexual displays. We phrase our model in terms of male bowerbirds either searching for or stealing resources (ornamental objects) valued by females, and compare the model findings with published studies of time allocation to various activities in different species of bowerbirds. The basic idea of the model, however, extends to cases where the resource is used less directly for the development of sexual ornamentation, such as males excluding others' access to food. We show that if males compete for resources used in sexual displays, intense female preference for high-quality displays can lead to poorer prospects for efficient choice by females. This is because males benefit from excluding others' access to resources used in displays, damaging the overall efficiency of resource use in the population, and the accuracy with which females can judge male ability to gain such resources. The evolution of female choice may therefore have a self-limiting nature when it poses a selection pressure on male resource acquisition.