We propose the coordination of many nodes by distributed communication. The idea is to switch attention from exchanging information to setting up cooperative action. This changes network communication into a new problem. For example, suppose one wishes to have each of m nodes perform a different task, where the distribution of tasks is uniform over the m! assignments. Node 1 is specified by nature to do task i, say. How much information must be sent to each of the nodes to achieve this distribution?
In general, how much information {Rij}, j = 1, 2..., m, must be conveyed to achieve a specified joint distribution p(y1; y2; :::; ym) at the nodes, given that the values at a certain subset of the nodes is specified? Once the set of all distributions achievable for a given description region {Rij} is found, rate distortion theory becomes a special case. Furthermore, the broadcast channel and all the other multiuser channels in network information theory can be revisited. Here we are interested, not in the number of bits that can be distributed over this network, but rather the set of all coordinated actions that can be achieved.
This should have applications in distributed task assignment in a computer, coherent transmission of relay information, cooperative communication, coordination of sensors in a sensor network, and cooperative behavior in a society. What does it take to generate cooperative behavior?
Intellectual merit of activity: The proposed work requires investigating the fundamentals of how joint distributions are created under constraints. This should be interesting as well as reasonably fundamental. It will provide guidance to the efficient creation of coordination in networks.
Broader impacts resulting from proposed activity: Understanding the generation of joint actions should have impact on communication, coordination of sensor networks, distributed computation, control systems and social networks.
