Bottleneck Routing Games with Low Price of Anarchy

We study {\em bottleneck routing games} where the social cost is determined by the worst congestion on any edge in the network. In the literature, bottleneck games assume player utility costs determined by the worst congested edge in their paths. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the size of the network. In order to obtain smaller price of anarchy we introduce {\em exponential bottleneck games} where the utility costs of the players are exponential functions of their congestions. We find that exponential bottleneck games are very efficient and give a poly-log bound on the price of anarchy: $O(\log L \cdot \log |E|)$, where $L$ is the largest path length in the players' strategy sets and $E$ is the set of edges in the graph. By adjusting the exponential utility costs with a logarithm we obtain games whose player costs are almost identical to those in regular bottleneck games, and at the same time have the good price of anarchy of exponential games.Comment: 12 page

Routing Games over Time with FIFO policy

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a \emph{first-in-first-out} queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.Comment: Submission to WINE-2017 Deadline was August 2nd AoE, 201

Uncertainty in Multi-Commodity Routing Networks: When does it help?

We study the equilibrium behavior in a multi-commodity selfish routing game with many types of uncertain users where each user over- or under-estimates their congestion costs by a multiplicative factor. Surprisingly, we find that uncertainties in different directions have qualitatively distinct impacts on equilibria. Namely, contrary to the usual notion that uncertainty increases inefficiencies, network congestion actually decreases when users over-estimate their costs. On the other hand, under-estimation of costs leads to increased congestion. We apply these results to urban transportation networks, where drivers have different estimates about the cost of congestion. In light of the dynamic pricing policies aimed at tackling congestion, our results indicate that users' perception of these prices can significantly impact the policy's efficacy, and "caution in the face of uncertainty" leads to favorable network conditions.Comment: Currently under revie

Utilitarian resource assignment

This paper studies a resource allocation problem introduced by Koutsoupias and Papadimitriou. The scenario is modelled as a multiple-player game in which each player selects one of a finite number of known resources. The cost to the player is the total weight of all players who choose that resource, multiplied by the ``delay'' of that resource. Recent papers have studied the Nash equilibria and social optima of this game in terms of the $L_\infty$ cost metric, in which the social cost is taken to be the maximum cost to any player. We study the $L_1$ variant of this game, in which the social cost is taken to be the sum of the costs to the individual players, rather than the maximum of these costs. We give bounds on the size of the coordination ratio, which is the ratio between the social cost incurred by selfish behavior and the optimal social cost; we also study the algorithmic problem of finding optimal (lowest-cost) assignments and Nash Equilibria. Additionally, we obtain bounds on the ratio between alternative Nash equilibria for some special cases of the problem.Comment: 19 page