Networks are largely viewed as a medium for communication from transmitters to receivers. More generally a network can be used as a medium to enable coordinated action between the entities represented by its nodes. Of particular interest is the simulation of joint distributions over networks, which is of interest both in security as in the creation of a shared secret key between some of the nodes of the network, and in strategic scenarios where the network, as player in a game, may need to jointly randomize the actions of the entities that comprise it. There has been considerable recent interest and progress in the information theory community on the problem of simulation of joint distributions over networks. We will discuss some of this progress, present some of our new results, and discuss some of the open problems in this area (based on joint work with Vivek Borkar, Amin Aminzadeh Gohari, and Sudeep Kamath).
