  Robots and autonomous systems must interact with one another and their
environment to provide high-quality services to their users. Dynamic game
theory provides an expressive theoretical framework for modeling scenarios
involving multiple agents with differing objectives interacting over time. A
core challenge when formulating a dynamic game is designing objectives for each
agent that capture desired behavior. In this paper, we propose a method for
inferring parametric objective models of multiple agents based on observed
interactions. Our inverse game solver jointly optimizes player objectives and
continuous-state estimates by coupling them through Nash equilibrium
constraints. Hence, our method is able to directly maximize the observation
likelihood rather than other non-probabilistic surrogate criteria. Our method
does not require full observations of game states or player strategies to
identify player objectives. Instead, it robustly recovers this information from
noisy, partial state observations. As a byproduct of estimating player
objectives, our method computes a Nash equilibrium trajectory corresponding to
those objectives. Thus, it is suitable for downstream trajectory forecasting
tasks. We demonstrate our method in several simulated traffic scenarios.
Results show that it reliably estimates player objectives from a short sequence
of noise-corrupted partial state observations. Furthermore, using the estimated
objectives, our method makes accurate predictions of each player's trajectory.
