  We study PAC learnability and PAC stabilizability of Hedonic Games (HGs),
i.e., efficiently inferring preferences or core-stable partitions from samples.
We first expand the known learnability/stabilizability landscape for some of
the most prominent HGs classes, providing results for Friends and Enemies
Games, Bottom Responsive, and Anonymous HGs. Then, having a broader view in
mind, we attempt to shed light on the structural properties leading to
learnability/stabilizability, or lack thereof, for specific HGs classes. Along
this path, we focus on the fully expressive Hedonic Coalition Nets
representation of HGs. We identify two sets of conditions that lead to
efficient learnability, and which encompass all of the known positive
learnability results. On the side of stability, we reveal that, while the
freedom of choosing an ad hoc adversarial distribution is the most obvious
hurdle to achieving PAC stability, it is not the only one. First, we show a
distribution independent necessary condition for PAC stability. Then, we focus
on $\W$-games, where players have individual preferences over other players and
evaluate coalitions based on the least preferred member. We prove that these
games are PAC stabilizable under the class of bounded distributions, which
assign positive probability mass to all coalitions. Finally, we discuss why
such a result is not easily extendable to other HGs classes even in this
promising scenario. Namely, we establish a purely computational property
necessary for achieving PAC stability.
