Improving Selfish Routing for Risk-Averse Players

Abstract

We investigate how and to which extent one can exploit risk-aversion and modify the perceived cost of the players in selfish routing so that the Price of Anarchy ($\mathrm {PoA}$) 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 risk-aversion. We adopt the model of $\gamma$-modifiable routing games, a variant of routing games with restricted tolls. We prove that computing the best $\gamma$-enforceable flow is $\mathrm {NP}$-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 $\gamma$-enforceable flow whose $\mathrm {PoA}$ improves fast as $\gamma$ increases. We show that the complexity of computing such a $\gamma$-enforceable flow is determined by the complexity of computing a Nash flow of the original game. Moreover, we prove that the $\mathrm {PoA}$ of this flow is best possible in the worst-case, in the sense that there are instances where (i) the best $\gamma$-enforceable flow has the same $\mathrm {PoA}$, and (ii) considering more flexible modifications does not lead to any further improvement.

This research was supported by the project Algorithmic Game Theory, co-financed by the European Union (European Social Fund) and Greek national funds, through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework - Research Funding Program: THALES, investing in knowledge society through the European Social Fund, and by grant NSF CCF 1216103.