Robust bottleneck routing games

Network routing games have attracted a lot of attention over the last years. However, most of the work assumes that the users have complete knowledge about the data in the network, in particular, about the precise travel times over the links. In this article, we address the more realistic case that users only know lower and upper bounds for the travel times and learn about the actual realization later. Thus, users cannot expect to choose a strategy which is optimal for each realization (scenario). This situation leads to combining concepts from robust optimization with algorithmic game theory. Specifically, we study the case where each user wants to minimize her regret, which is defined to be the worst‐case difference of her bottleneck objective (the cost of her most expensive resource) to the optimum attainable value given a priori knowledge about the actual scenario. We show that in robust bottleneck routing games, equilibria do not always exist, but the existence can be guaranteed under the restriction that the problem is symmetric and the intervals of uncertainty have constant length. We prove that in general it is NP‐hard to decide whether a given instance has a robust equilibrium. In the case of constant‐length intervals of uncertainty, a robust equilibrium can be computed efficiently (in the symmetric case). We also investigate the Price of Robustness, which formally quantifies the lack of performance due to uncertainty and give a tight bound.