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Improving selfish routing for risk-averse players. (English) Zbl 1404.91050
Markakis, Evangelos (ed.) et al., Web and internet economics. 11th international conference, WINE 2015, Amsterdam, The Netherlands, December 9–12, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-48994-9/pbk; 978-3-662-48995-6/ebook). Lecture Notes in Computer Science 9470, 328-342 (2015).
Summary: 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 (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 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 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 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 PoA, and (ii) considering more flexible modifications does not lead to any further improvement.
For the entire collection see [Zbl 1326.68026].

91A43 Games involving graphs
91B16 Utility theory
Full Text: DOI
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