Communication in networks for coordinating behavior

In this work, we develop elements of a theory of coordination in networks using tools from information theory. We ask questions of this nature: If three different tasks are to be performed in a shared effort between three people, but one of them is randomly assigned his responsibility, how much must he tell the others about his assignment? If two players of a multiplayer game wish to collaborate, how should they best use communication to generate their actions? More generally, we ask for the set of all possible joint distributions p(x1, ..., x m) of actions at the nodes of a network when rate-limited communication is allowed between the nodes. Several networks are solved, including arbitrarily large cascade networks. Distributed coordination can be the solution to many problems such as distributed games, distributed control, and establishing mutual information bounds on the physical influence of one part of a system on another.