Dynamic Information Manipulation Game

We propose a dynamic information manipulation game (DIMG) to investigate the incentives of an information manipulator (IM) to influence the transition rules of a partially observable Markov decision process (POMDP). DIMG is a hierarchical game where the upper-level IM stealthily designs the POMDP's joint state distributions to influence the lower-level controller's actions. DIMG's fundamental feature is characterized by a stagewise constraint that ensures the consistency between the unobservable marginals of the manipulated and the original kernels. In an equilibrium of information distortion, the IM minimizes cumulative cost that depends on the controller's informationally manipulated actions generated by the optimal policy to the POMDP. We discuss ex ante and interim manipulation schemes and show their connections. The effect of manipulation on the performance of control policies is analyzed through its influence on belief distortion.