  With autonomous vehicles (AV) set to integrate further into regular human
traffic, there is an increasing consensus on treating AV motion planning as a
multi-agent problem. However, the traditional game-theoretic assumption of
complete rationality is too strong for human driving, and there is a need for
understanding human driving as a \emph{bounded rational} activity through a
behavioural game-theoretic lens. To that end, we adapt four metamodels of
bounded rational behaviour: three based on Quantal level-k and one based on
Nash equilibrium with quantal errors. We formalize the different solution
concepts that can be applied in the context of hierarchical games, a framework
used in multi-agent motion planning, for the purpose of creating game theoretic
models of driving behaviour. Furthermore, based on a contributed dataset of
human driving at a busy urban intersection with a total of approximately 4k
agents and 44k decision points, we evaluate the behaviour models on the basis
of model fit to naturalistic data, as well as their predictive capacity. Our
results suggest that among the behaviour models evaluated, at the level of
maneuvers, modeling driving behaviour as an adaptation of the Quantal level-k
model with level-0 behaviour modelled as pure rule-following provides the best
fit to naturalistic driving behaviour. At the level of trajectories, bounds
sampling of actions and a maxmax non-strategic models is the most accurate
within the set of models in comparison. We also find a significant impact of
situational factors on the performance of behaviour models.
