  In 2013, Lu and Ren \cite {luren} considered anticipated backward stochastic
differential equations driven by finite state, continuous time Markov chain
noise and established the existence and uniqueness of the solutions of these
equations and a scalar comparison theorem. In this paper, we provide an
estimate for their solutions and study the duality between these equations and
stochastic differential delayed equations with Markov chain noise. Finally we
derive another comparison theorem for these solutions depending only on the two
drivers.
