  We consider a dynamic Bayesian persuasion setting where a single long-lived
sender persuades a stream of ``short-lived'' agents (receivers) by sharing
information about a payoff-relevant state. The state transitions are Markovian
and the sender seeks to maximize the long-run average reward by committing to a
(possibly history-dependent) signaling mechanism. While most previous studies
of Markov persuasion consider exogenous agent beliefs that are independent of
the chain, we study a more natural variant with endogenous agent beliefs that
depend on the chain's realized history. A key challenge to analyze such
settings is to model the agents' partial knowledge about the history
information. We analyze a Markov persuasion process (MPP) under various
information models that differ in the amount of information the receivers have
about the history of the process. Specifically, we formulate a general
partial-information model where each receiver observes the history with an
$\ell$ period lag. Our technical contribution start with analyzing two
benchmark models, i.e., the full-history information model and the no-history
information model. We establish an ordering of the sender's payoff as a
function of the informativeness of agent's information model (with no-history
as the least informative), and develop efficient algorithms to compute optimal
solutions for these two benchmarks. For general $\ell$, we present the
technical challenges in finding an optimal signaling mechanism, where even
determining the right dependency on the history becomes difficult. To bypass
the difficulties, we use a robustness framework to design a "simple"
\emph{history-independent} signaling mechanism that approximately achieves
optimal payoff when $\ell$ is reasonably large.
