Path deviations outperform approximate stability in heterogeneous congestion games

We consider non-atomic network congestion games with heterogeneous players where the latencies of the paths are subject to some bounded deviations. This model encompasses several well-studied extensions of the classical Wardrop model which incorporate, for example, risk-aversion, altruism or travel time delays. Our main goal is to analyze the worst-case deterioration in social cost of a perturbed Nash flow (i.e., for the perturbed latencies) with respect to an original Nash flow. We show that for homogeneous players perturbed Nash flows coincide with approximate Nash flows and derive tight bounds on their inefficiency. In contrast, we show that for heterogeneous populations this equivalence does not hold. We derive tight bounds on the inefficiency of both perturbed and approximate Nash flows for arbitrary player sensitivity distributions. Intuitively, our results suggest that the negative impact of path deviations (e.g., caused by risk-averse behavior or latency perturbations) is less severe than approximate stability (e.g., caused by limited responsiveness or bounded rationality). We also obtain a tight bound on the inefficiency of perturbed Nash flows for matroid congestion games and homogeneous populations if the path deviations can be decomposed into edge deviations. In particular, this provides a tight bound on the Price of Risk-Aversion for matroid congestion games

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

Change-Averse Nash Equilibria in Congestion Games

Εισάγουμε ένα νέο μοντέλο στα Παίγνια Συμφόρησης, όπου οι παίκτες επιλέγουν τη στρατηγική τους σύμφωνα με το νέο κόστος τους, όπως επίσης και με τη διαφορά της υφιστάμενής τους κατάστασης σε σχέση με τη νέα. Το τελευταίο κομμάτι της διαδικασίας απόφασης βασίζεται στην υπόθεση ότι παίκτες που σκέφτονται να κάνουν μια μεγάλη αλλαγή έχουν μικρότερη τάση να την κάνουν, παρά παίκτες με μικρότερη αλλαγή. Αυτό το μοντέλο έχει αναλογίες με τις ε-προσεγγιστικές ισορροπίες. Μπορούμε εύκολα να δούμε ότι το νέο αυτό μοντέλο περιέχει ένα πλουσιότερο σύνολο ισορροπιών σε σχέση με τις ε-προσεγγιστικές ισορροπίες. Ο Χριστοδούλου et al. αποδεικνύουν ότι σε σχέση με γραμμικά παιγνία συμφόρησης, έχουμε καλά φράγματα στο Τίμημα της Αναρχίας. Αποδεικνύουμε ότι όμοια αποτελέσματα ισχύουν και στη δική μας περίπτωση. Επίσης, αποδεικνύουμε ότι οι παίκτες συγκλίνουν σε μια τέτοια ισορροπία και μάλιστα συγκλίνουν με αποδεκτή ταχύτητα.We introduce a new model in Congestion Games, where the players choose their strategy according to the new cost they incur, as well as the difference between their current state and the new state they are considering. The latter part of the decision-making process is based on the assumption that players who are considering a signicant change are less prone to take it, than they do on a similar choice. This model has analogies with ϵ approximate equilibria. We can easily see that this new model provides a richer set of equilibria than approximate equilibria. Christodoulou et al. prove that as far as Linear Congestion Games are concerned, we have good bounds on the Price of Anarchy. We prove that similar results are true in our case. We also prove that players do actually converge on such an equilibrium and relatively quickly