Decentralized Control of Two Agents with Nested Accessible Information

We investigate a decentralized stochastic control problem with two agents, where a part of the memory of the second agent is always available to the first agent. We derive a structural form for optimal control strategies that allows us to restrict their domain to a set that does not grow in size with time, and subsequently, utilize them for systems with arbitrarily long time horizons. We utilize our results to present a common information based dynamic program (DP). However, we observe that it is computationally challenging to use this DP to derive control strategies because they are functions of a vector of probability mass functions. Thus, we present simplified strategies for a special case of our model, and an approximation technique that can be used to implement our results by trading a gain in computational tractability with a loss in optimality.