recovering principled behavior in a new game. Thus, we require a form of rationality.

The players in a game are [****]{} with respect to deviation set ${\Phi}$ if they prefer joint-strategy ${\sigma^{{\Gamma}}}$ over joint strategies ${\acute{\sigma}^{{\Gamma}}}$ when $$\begin{aligned}
{\operatorname{Regret}^{{\Gamma}}_{{\Phi}}({\sigma^{{\Gamma}}}|{w^*})} & < {\operatorname{Regret}^{{\Gamma}}_{{\Phi}}({\acute{\sigma}^{{\Gamma}}}|{w^*})}.\end{aligned}$$

Our rationality assumption states that the players are driven to minimize their regret. It is not necessarily the case that they indeed have low or no regret, but simply that they can evaluate their preferences and that they prefer joint strategies with low regret. Through this assumption, we will be able to reason about the players’ behavior solely through the game’s features; this is what leads to the improved statistical properties of our approach.

As agents’ true preferences ${w^*}$ are unknown, we consider an encompassing assumption that requires that estimated behavior satisfy this property for all possible utility weights. A prediction ${\hat{\sigma}^{{\Gamma}}}$ is [****]{} with respect to deviation set ${\Phi}$ if $$\begin{aligned}
\forall {w}\in{V},\;\;{\operatorname{Regret}^{{\Gamma}}_{{\Phi}}({\hat{\sigma}^{{\Gamma}}}|{w})}& \le {\operatorname{Regret}^{{\Gamma}}_{{\Phi}}({{\sigma^{{\Gamma}}}}|{w})}.\end{aligned}$$

This assumption is similar in spirit to the utility matching assumption employed by inverse optimal control techniques in single-agent settings. As in those settings, we have an [*if and only if*]{} guarantee relating rationality and strong rationality [@abbeel2004; @ziebart2008].

If a prediction 