Coordination Capacity

Abstract

We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex Notation="TeX">$\{R_{i,j}\}$</tex> </formula></emphasis> between the nodes, we ask what is the set of all achievable joint distributions <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"> <tex Notation="TeX">$p(x_{1},\ldots ,x_{m})$</tex></formula></emphasis> of actions at the nodes of the network. Several networks are solved, including arbitrarily large cascade networks. Distributed cooperation can be the solution to many problems such as distributed games, distributed control, and establishing mutual information bounds on the influence of one part of a physical system on another.