Urban Driving Games with Lexicographic Preferences and Socially Efficient Nash Equilibria

We describe Urban Driving Games (UDGs) as a particular class of differential games that model the interactions and incentives of the urban driving task. The drivers possess a "communal" interest, such as not colliding with each other, but are also self-interested in fulfilling traffic rules and personal objectives. Subject to their physical dynamics, the preference of the agents is expressed via a lexicographic relation that put as first priority the shared objective of not colliding. Under mild assumptions, we show that UDGs have the structure of a lexicographic ordinal potential game which allows to prove several interesting properties. Namely, socially efficient equilibria can be find solving a single (lexicographic) optimal control problem and iterated best response schemes have desirable convergence guarantees.