happiness or individual well-being. We assume that the players’ utility is a common linear function of the utility features. This will allow us to treat the players anonymously should we so desire. One can expand the utility feature space if separate utility functions are desired. We write the utility for player ${i}$ at outcome ${a}$ under utility function ${w}\in{V}$ as $$\begin{aligned}
{{u^{{\Gamma}}_{{i}}}({a}|{w})} &={\langle {{u^{{\Gamma}}_{{i}}}({a})},{w}\rangle}.\end{aligned}$$

In contrast to the standard definition of normal-form games, where the utility functions for game outcomes are known, in this work we assume that the [****]{}, formed by ${w^*}$, which governs observed behavior, is unknown. This allows us to model real-world scenarios where a cardinal utility is not available or is subject to personal taste. Consider, for instance, a scenario where multiple drivers each choose a route among shared roads. Each outcome, which specifies a travel plan for all drivers, has a variety of easily measurable quantities that may impact the utility of a driver, such as travel time, distance, average speed, number of intersections and so on, but how these quantities map to utility depends on the internal preferences of the drivers.

We model the players using a [****]{}, ${\sigma^{{\Gamma}}}\in{\Delta_{{\mathcal A}}}$, which is a distribution 