Decentralized control of a stochastic dynamic resource allocation problem

Abstract

This paper concerns decentralized control of a certain stochastic and dynamic resource allocation problem. The system consists of two agents, a pricing agent and a service agent. The pricing agent controls the customer arrival rate by dynamically setting prices while the service agent controls the rate at which customers are served. The distinguishing feature of our setup is that the pricing and service agents know different subcomponents of the model but are unwilling or unable to reveal their knowledge of the system to the other agent (or a centralized controller). This means that joint optimization over pricing and service policies is not possible since there is no single agent with knowledge of all relevant system parameters. Within this setup, we show that the centralized optimal pricing and service policies can still be constructed. Specifically, the integrated problem can be decoupled into a dynamic pricing problem (for the pricing agent) and a service rate control problem (for the service agent), and that these single-agent problems can be specified so as to deliver the centralized optimal policies. We also present an iterative algorithm which enables pricing and service agents to construct the centralized optimal policies without having to reveal private knowledge about the system to the other agent.