Improving Selfish Routing for Risk-Averse Players.

Dimitris Fotakis, Dimitris Kalimeris, Thanasis Lianeas

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. This is a preview of subscription content, log in to check access.