Structural Results for Decentralized Stochastic Control with a Word-of-Mouth Communication

In this paper, we analyze a network of agents that communicate through the "word of mouth," in which, every agent communicates only with its neighbors. We introduce the prescription approach, present some of its properties and show that it leads to a new information state. We also state preliminary structural results for optimal control strategies in systems that evolve using word-of-mouth communication. The proposed approach can be generalized to analyze several decentralized systems.