the tools necessary to introduce our approach for imitation learning in multi-agent settings. We start by assuming a notion of rationality on the part of the game’s players. By leveraging this assumption, we will then derive an estimation procedure with much better statistical properties than methods that are unaware of the game’s structure.

Rationality and the ICE Polytope
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Let $\{{{a}^{{t}}}\}_{{t}=1}^{{T}}$ be a sequence of ${T}$ independent observations of behavior in game ${\Gamma}$ distributed according to ${{\sigma^{{\Gamma}}}}$, the players’ [****]{}. We call the empirical distribution of the observations, ${\tilde{\sigma}^{{\Gamma}}}$, the [****]{}.

We aim to learn a distribution ${\hat{\sigma}^{{\Gamma}}}$, called the [****]{}, an estimation of the true behavior from these demonstrations. Moreover, we would like our learning procedure to extract the motives for the behavior so that we may imitate the players in similarly structured, but unobserved games. Initially, let us consider just the estimation problem. While deriving our method, we will assume we have access to the players’ true behavior. Afterwards, we will analyze the error introduced by approximating from the demonstrations.

Imitation appears hard barring further assumptions. In particular, if the agents are unmotivated or their intentions are not coerced by the observed game, there is little hope of 