In building intelligent network agents, computer scientists may employ a variety of different design strategies, and their design decisions can have a significant effect on the ultimate nature of network interactions. Some agent designs are "cooperative," and populations of agents based on them would be able to interact smoothly, effectively utilizing network resources. In contrast, other agent designs can lead to ineffective and wasteful competition for network resources, resulting in massive bottlenecks and unacceptable access delays. We focus here on a particular design question, the multiple-access problem: if an agent seeking a piece of information knows of several sites that have, or might have, that information, how many queries should it issue, and when? We provide a formal analysis that demonstrates the viability of cooperative responses to this question. We then discuss the limitations of this analysis and describe a simulation system we are building to study more general versions of the problem.