  Many decentralized and networked control problems involve decision makers
which have either misaligned criteria or subjective priors. In the context of
such a setup, in this paper we consider binary signaling problems in which the
decision makers (the transmitter and the receiver) have subjective priors
and/or misaligned objective functions. Depending on the commitment nature of
the transmitter to his policies, we formulate the binary signaling problem as a
Bayesian game under either Nash or Stackelberg equilibrium concepts and
establish equilibrium solutions and their properties. In addition, the effects
of subjective priors and costs on Nash and Stackelberg equilibria are analyzed.
It is shown that there can be informative or non-informative equilibria in the
binary signaling game under the Stackelberg assumption, but there always exists
an equilibrium. However, apart from the informative and non-informative
equilibria cases, under certain conditions, there does not exist a Nash
equilibrium when the receiver is restricted to use deterministic policies. For
the corresponding team setup, however, an equilibrium typically always exists
and is always informative. Furthermore, we investigate the effects of small
perturbations in priors and costs on equilibrium values around the team setup
(with identical costs and priors), and show that the Stackelberg equilibrium
behavior is not robust to small perturbations whereas the Nash equilibrium is.
