Coordination Capacity

TL;DR

This paper develops a theoretical framework for understanding how dependence among network nodes can be established under communication constraints, focusing on the achievable joint distributions of actions in various network topologies.

Contribution

It introduces a novel approach to analyze cooperation in networks based on dependence rather than information distribution, solving several network configurations including large cascades.

Findings

Characterizes achievable joint distributions in networks with communication constraints

Solves for various network topologies including large cascade networks

Provides bounds relevant to distributed control and information influence

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 {R_{i,j}} between the nodes, we ask what is the set of all achievable joint distributions p(x1, ..., xm) 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.