  When robots share the same workspace with other intelligent agents (e.g.,
other robots or humans), they must be able to reason about the behaviors of
their neighboring agents while accomplishing the designated tasks. In practice,
frequently, agents do not exhibit absolutely rational behavior due to their
limited computational resources. Thus, predicting the optimal agent behaviors
is undesirable (because it demands prohibitive computational resources) and
undesirable (because the prediction may be wrong). Motivated by this
observation, we remove the assumption of perfectly rational agents and propose
incorporating the concept of bounded rationality from an information-theoretic
view into the game-theoretic framework. This allows the robots to reason other
agents' sub-optimal behaviors and act accordingly under their computational
constraints. Specifically, bounded rationality directly models the agent's
information processing ability, which is represented as the KL-divergence
between nominal and optimized stochastic policies, and the solution to the
bounded-optimal policy can be obtained by an efficient importance sampling
approach. Using both simulated and real-world experiments in multi-robot
navigation tasks, we demonstrate that the resulting framework allows the robots
to reason about different levels of rational behaviors of other agents and
compute a reasonable strategy under its computational constraint.
