  We consider a two-player dynamic information design problem between a
principal and a receiver -- a game is played between the two agents on top of a
Markovian system controlled by the receiver's actions, where the principal
obtains and strategically shares some information about the underlying system
with the receiver in order to influence their actions. In our setting, both
players have long-term objectives, and the principal sequentially commits to
their strategies instead of committing at the beginning. Further, the principal
cannot directly observe the system state, but at every turn they can choose
randomized experiments to observe the system partially. The principal can share
details about the experiments to the receiver. For our analysis we impose the
truthful disclosure rule: the principal is required to truthfully announce the
details and the result of each experiment to the receiver immediately after the
experiment result is revealed. Based on the received information, the receiver
takes an action when its their turn, with the action influencing the state of
the underlying system. We show that there exist Perfect Bayesian equilibria in
this game where both agents play Canonical Belief Based (CBB) strategies using
a compressed version of their information, rather than full information, to
choose experiments (for the principal) or actions (for the receiver). We also
provide a backward inductive procedure to solve for an equilibrium in CBB
strategies.
