Dynamic incentive design in multi-stage linear-Gaussian games with asymmetric information: A common information based approach

We study a finite-horizon multi-stage N + 1-player incentive design problem with a hierarchical information structure at each stage. Each controller (or player) is assumed to have a stagewise additive cost function, in which the cost to a controller at any stage depends on the state of the system at that stage and the actions taken by all the controllers at that stage. We also assume that the controllers do not necessarily acquire the same information at the beginning of each stage. This leads to a multi-stage incentive design problem with dynamic asymmetric information. During each stage, Controller 0 is assumed to have access to private information and actions of all controllers, and announces its control law so that it is in the best interest of other controllers to act in a specific manner. We introduce a new notion of dynamic incentive strategies, called common information based subgame-perfect incentive scheme (CISPIS), along the lines of subgame-perfect Nash equilibrium concept for perfect information games. We show that under certain sufficient conditions, the multi-stage incentive design problem admits a CISPIS. The control law of Controller 0 at every stage is affine in the actions of other controllers under this scheme.