We consider a finite-horizon discrete-time dynamic system jointly controlled by a designer and multiple agents, where the designer can influence the agents' actions through selective information disclosure. At each time step, the designer sends private messages to the agents from prespecified message spaces. The designer may also take an action that directly influences system dynamics and rewards. Each agent uses its received message and its own information to choose its action. We are interested in the setting where the designer would like to incentivize the agents to use prescribed strategies. We consider a notion of incentive compatibility that is based on sequential rationality at each realization of the common information among the designer and the agents. We consider both myopic and non-myopic agents and formulate the designer's problem as maximizing its total expected reward subject to the corresponding sequential rationality constraints. Under certain assumptions on the information structure, we obtain an equivalent reformulation of the designer's problem and develop a backward-inductive procedure based on a family of linear programs. For non-myopic agents, this procedure yields feasible solutions but need not be globally optimal for a general designer reward. For myopic agents, the procedure yields a globally optimal solution.

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