  A robot operating in isolation needs to reason over the uncertainty in its
model of the world and adapt its own actions to account for this uncertainty.
Similarly, a robot interacting with people needs to reason over its uncertainty
over the human internal state, as well as over how this state may change, as
humans adapt to the robot. This paper summarizes our own work in this area,
which depicts the different ways that probabilistic planning and game-theoretic
algorithms can enable such reasoning in robotic systems that collaborate with
people. We start with a general formulation of the problem as a two-player game
with incomplete information. We then articulate the different assumptions
within this general formulation, and we explain how these lead to exciting and
diverse robot behaviors in real-time interactions with actual human subjects,
in a variety of manufacturing, personal robotics and assistive care settings.
