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) wrt. the total latency is improved. The starting point is to introduce some 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 simple model of γ-modifiable routing games, a variant of selfish 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 γ-enforceable flow is determined by the complexity of computing a Nash flow for 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 improvement on the PoA.

中文翻译：

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为规避风险的玩家改善自私的路线

我们研究了人们可以如何以及在多大程度上利用风险规避并修改自私路由中参与者的感知成本，从而使无政府状态价格（PoA）降低。总延迟得以改善。起点是对边缘延迟引入一些小的随机扰动，以使预期的延迟不会改变，但是由于规避风险，玩家的感知成本会增加。我们采用γ可修改路由游戏的简单模型，这是收费受限的自私路由游戏的一种变体。我们证明计算最佳的γ强制流为N P-具有相似性等待时间和两类异类风险规避参与者的并行链接网络很难。从积极的一面，我们表明对于具有异构参与者的并行链接网络和具有同类参与者的串并联网络，存在结构良好的γ强制流，其PoA随着γ的增加而快速提高。我们表明，计算此类γ强制流的复杂性取决于计算原始游戏的Nash流的复杂性。此外，我们证明在某些情况下（i）最佳γ可强制执行的流程具有相同的PoA，并且（ii）考虑更灵活的修改不会导致PoA有所改善。