  We consider scenarios where a worker robot, who may be unaware of the human's
exact expectations, may have the incentive to deviate from a preferred plan
(e.g. safe but costly) when a human supervisor is not monitoring it. On the
other hand, continuous monitoring of the robot's behavior is often difficult
for humans because it costs them valuable resources (e.g., time, cognitive
overload, etc.). Thus, to optimize the cost of monitoring while ensuring the
robots follow the {\em safe} behavior and to assist the human to deal with the
possible unsafe robots, we model this problem in a game-theoretic framework of
trust. In settings where the human does not initially trust the robot,
pure-strategy Nash Equilibrium provides a useful policy for the human.
Unfortunately, we show the formulated game often lacks a pure strategy Nash
equilibrium. Thus, we define the concept of a trust boundary over the mixed
strategy space of the human and show that it helps to discover optimal
monitoring strategies. We conduct humans subject studies that demonstrate (1)
the need for coming up with optimal monitoring strategies, and (2) the benefits
of using strategies suggested by our approach.
