  Humans often assume that robots are rational. We believe robots take optimal
actions given their objective; hence, when we are uncertain about what the
robot's objective is, we interpret the robot's actions as optimal with respect
to our estimate of its objective. This approach makes sense when robots
straightforwardly optimize their objective, and enables humans to learn what
the robot is trying to achieve. However, our insight is that---when robots are
aware that humans learn by trusting that the robot actions are
rational---intelligent robots do not act as the human expects; instead, they
take advantage of the human's trust, and exploit this trust to more efficiently
optimize their own objective. In this paper, we formally model instances of
human-robot interaction (HRI) where the human does not know the robot's
objective using a two-player game. We formulate different ways in which the
robot can model the uncertain human, and compare solutions of this game when
the robot has conservative, optimistic, rational, and trusting human models. In
an offline linear-quadratic case study and a real-time user study, we show that
trusting human models can naturally lead to communicative robot behavior, which
influences end-users and increases their involvement.
