  The use of deceptive strategies is important for an agent that attempts not
to reveal his intentions in an adversarial environment. We consider a setting
in which a supervisor provides a reference policy and expects an agent to
follow the reference policy and perform a task. The agent may instead follow a
different, deceptive policy to achieve a different task. We model the
environment and the behavior of the agent with a Markov decision process,
represent the tasks of the agent and the supervisor with reachability
specifications, and study the synthesis of optimal deceptive policies for such
agents. We also study the synthesis of optimal reference policies that prevent
deceptive strategies of the agent and achieve the supervisor's task with high
probability. We show that the synthesis of optimal deceptive policies has a
convex optimization problem formulation, while the synthesis of optimal
reference policies requires solving a nonconvex optimization problem. We also
show that the synthesis of optimal reference policies is NP-hard.
