  We examine the routing problem for self-interested vehicles using stochastic
decision strategies. By approximating the road latency functions and a
non-linear variable transformation, we frame the problem as an aggregative
game. We characterize the approximation error and we derive a new monotonicity
condition for a broad category of games that encompasses the problem under
consideration. Next, we propose a semi-decentralized algorithm to calculate the
routing as a variational generalized Nash equilibrium and demonstrate the
solution's benefits with numerical simulations. In the particular case of
potential games, which emerges for linear latency functions, we explore a
receding-horizon formulation of the routing problem, showing asymptotic
convergence to destinations and analysing closed-loop performance dependence on
horizon length through numerical simulations.
