Improving Selfish Routing for Risk-Averse Players

We investigate how and to which extent one can exploit riskaversion and modify the perceived cost of the players in selfish routing so that the Price of Anarchy (PoA) is improved. We introduce small random perturbations to the edge latencies so that the expected latency does not change, but the perceived cost of the players increases due to riskaversion. We adopt the model of γ-modifiable routing games, a variant of routing games with restricted tolls. We prove that computing the best γ-enforceable flow is NP-hard for parallel-link networks with affine latencies and two classes of heterogeneous risk-averse players. On the positive side, we show that for parallel-link networks with heterogeneous players and for series-parallel networks with homogeneous players, there exists a nicely structured γ-enforceable flow whose PoA improves fast as γ increases. We show that the complexity of computing such a γenforceable flow is determined by the complexity of computing a Nash flow of the original game. Moreover, we prove that the PoA of this flow is best possible in the worst-case, in the sense that there are instances where (i) the best γ-enforceable flow has the same PoA, and (ii) considering more flexible modifications does not lead to any further improvement.