Pricing and selection of channels for remote state estimation using a Stackelberg game framework

We consider the communication channel pricing and selection problem in a networked control system. To encompass the sequentialized nature of the decision-making process, we use game theory and formulate a Stackelberg game framework, where the server first determines the channel pricing strategy, and the clients then make channel selection decisions. Both single-server-single-client (SSSC) scenario and single-server-multi-client (SSMC) scenario are discussed. The existence of an optimal stationary and deterministic policy for the clients is proved. We show that for the SSSC scenario, the server's optimal pricing strategy in terms of maximizing revenue is to ensure that the client uses the good channel all the time. For the SSMC scenario, it is assumed that the channel price remains invariant. As a consequence, each client has an optimal policy with threshold structure. Some properties of the optimal policy pair for both scenarios are obtained. Simulation results confirm the structure and properties of both the server and clients' optimal strategies.