Under certain circumstances, the presumption that universal access to information infrastructure leads to greater equality of resources is incorrect. In fact, greater inequality can occur. This argument and several related propositions are explored through a formal theoretic~d model built on lbur simple assumptions: one cannot converse with everyone at the same time, information can be shared without loss, private information resources are not all the same, and agents can create new information in proportion to how much they know. The model rigorously explains how inter-agent infrastructure can be used to help the "rich get richer" and also why "it's not just what you know but whom you know." This theoretical framework is extensible and readily applied to real situations.