  We present a new method for multi-agent planning involving human drivers and
autonomous vehicles (AVs) in unsignaled intersections, roundabouts, and during
merging. In multi-agent planning, the main challenge is to predict the actions
of other agents, especially human drivers, as their intentions are hidden from
other agents. Our algorithm uses game theory to develop a new auction, called
GamePlan, that directly determines the optimal action for each agent based on
their driving style (which is observable via commonly available sensors).
GamePlan assigns a higher priority to more aggressive or impatient drivers and
a lower priority to more conservative or patient drivers; we theoretically
prove that such an approach is game-theoretically optimal prevents collisions
and deadlocks. We compare our approach with prior state-of-the-art auction
techniques including economic auctions, time-based auctions (first-in
first-out), and random bidding and show that each of these methods result in
collisions among agents when taking into account driver behavior. We compare
with methods based on DRL, deep learning, and game theory and present our
benefits over these approaches. Finally, we show that our approach can be
implemented in the real-world with human drivers.
