a compactly expressed utility function that [*rationalizes*]{} observed behavior: that is, identify rewards for which the demonstrated behavior is optimal and then leverage these rewards for future prediction. Unfortunately, the problem is fundamentally ill-posed: in general, many reward functions can make behavior seem rational, and in fact, the trivial, everywhere zero reward function makes [**all**]{} behavior appear rational [@ng2000algorithms]. Further, after removing such trivial reward functions, there may be [**no**]{} reward function for which the demonstrated behavior is optimal as agents may be imperfect or the world they operate in may only be approximately represented.

In the single-agent decision-theoretic setting, inverse optimal control methods have been used to bridge this gap between the prescriptive frameworks and predictive applications [@abbeel2004; @ratliff2006; @ziebart2008; @ziebart2010]. Successful applications include learning and prediction tasks in personalized vehicle route planning [@ziebart2008], predictive cursor control [@ziebart2012], robotic crowd navigation [@henry2010], quadruped foot placement and grasp selection [@ratliff2009]. A reward function is learned by these techniques that both explains demonstrated behavior and approximates the optimality criteria of decision-theoretic frameworks.

As these methods only capture a single reward function and do not reason about competitive or cooperative motives, inverse optimal control proves inadequate for modeling the strategic interactions of 