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

The Complexity of Welfare Maximization in Congestion Games

We investigate issues of complexity related to welfare maximization in congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general congestion games, and we examine several variants of the problem concerning the structure of the game and the properties of its associated cost functions. Many of these problem variants turn out to be NP-hard, and some are hard to approximate to within any finite factor, unless P = NP. We also identify several versions of the problem that are solvable in polynomial time.United States. Dept. of Energy (Grant Number: DE-AC52-07NA27344)Lawrence Livermore National Laboratory (Grant Number: LLNL-JRNL-410585)United States. Office of Naval Research (Grant Number: N000141110056

On the existence of Nash equilibria in strategic search games

We consider a general multi-agent framework in which a set of n agents are roaming a network where m valuable and sharable goods (resources, services, information ....) are hidden in m different vertices of the network. We analyze several strategic situations that arise in this setting by means of game theory. To do so, we introduce a class of strategic games that we call strategic search games. In those games agents have to select a simple path in the network that starts from a predetermined set of initial vertices. Depending on how the value of the retrieved goods is splitted among the agents, we consider two game types: finders-share in which the agents that find a good split among them the corresponding benefit and firsts-share in which only the agents that first find a good share the corresponding benefit. We show that finders-share games always have pure Nash equilibria (pne ). For obtaining this result, we introduce the notion of Nash-preserving reduction between strategic games. We show that finders-share games are Nash-reducible to single-source network congestion games. This is done through a series of Nash-preserving reductions. For firsts-share games we show the existence of games with and without pne. Furthermore, we identify some graph families in which the firsts-share game has always a pne that is computable in polynomial time.Peer ReviewedPostprint (author’s final draft

Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201

The Value of Information in Selfish Routing

Path selection by selfish agents has traditionally been studied by comparing social optima and equilibria in the Wardrop model, i.e., by investigating the Price of Anarchy in selfish routing. In this work, we refine and extend the traditional selfish-routing model in order to answer questions that arise in emerging path-aware Internet architectures. The model enables us to characterize the impact of different degrees of congestion information that users possess. Furthermore, it allows us to analytically quantify the impact of selfish routing, not only on users, but also on network operators. Based on our model, we show that the cost of selfish routing depends on the network topology, the perspective (users versus network operators), and the information that users have. Surprisingly, we show analytically and empirically that less information tends to lower the Price of Anarchy, almost to the optimum. Our results hence suggest that selfish routing has modest social cost even without the dissemination of path-load information.Comment: 27th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2020

Evacuation planning under selfish evacuation routing

In case of an evacuation a large number of evacuees must be routed through a street network to let them leave the endangered area and reach safe places. In such a situation a lot of evacuees use the street network in a short time span and so the network capacity will be insufficient. With an evacuation plan the traffic could be guided through the network for a better use of network capacity. But to implement the solution planned by a central decision maker, optimal routes must be communicated to all network users, which lead to a high communication effort. Furthermore, it must be ensured that the evacuees take the given routes. But a lot of people do not follow the instructions from authorities in a panic situation. They do what they assume is best for themselves. Such selfish behaviour leads to a suboptimal distribution of traffic and results in congestion. In this thesis we present a concept to guide the evacuees through the network without determining optimal routes for all network users. With the blockage of street sections we force the evacuees to use other routes than the preferred ones but give them the possibility to choose their routes on their own. The thesis presents different mathematical model formulations and heuristic for the described problem. In a comprehensive computational study, with real world examples, the functionality of the presented concept and methods are tested

The complexity of pure nash equilibria in max-congestion games

We study Network Max-Congestion Games (NMC games, for short), a class of network games where each player tries to minimize the most congested edge along the path he uses as strategy. We focus our study on the complexity of computing a pure Nash equilibria in this kind of games. We show that, for single-commodity games with non-decreasing delay functions, this problem is in P when either all the paths from the source to the target node are disjoint or all the delay functions are equal. For the general case, we prove that the computation of a PNE belongs to the complexity class PLS through a new technique based on generalized ordinal potential functions and a slightly modified definition of the usual local search neighborhood. We further apply this technique to a different class of games (which we call Pareto-efficient) with restricted cost functions. Finally, we also prove some PLS-hardness results, showing that computing a PNE for Pareto-efficient NMC games is indeed a PLS-complete problem

The complexity of pure nash equilibria in max-congestion games

We study Network Max-Congestion Games (NMC games, for short), a class of network games where each player tries to minimize the most congested edge along the path he uses as strategy. We focus our study on the complexity of computing a pure Nash equilibria in this kind of games. We show that, for single-commodity games with non-decreasing delay functions, this problem is in P when either all the paths from the source to the target node are disjoint or all the delay functions are equal. For the general case, we prove that the computation of a PNE belongs to the complexity class PLS through a new technique based on generalized ordinal potential functions and a slightly modified definition of the usual local search neighborhood. We further apply this technique to a different class of games (which we call Pareto-efficient) with restricted cost functions. Finally, we also prove some PLS-hardness results, showing that computing a PNE for Pareto-efficient NMC games is indeed a PLS-complete problem

A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation