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.
Selfish routing on dynamic flows over time is used to model scenarios that vary with time in which individual agents act in their best interest. In this paper we provide a survey of a particular dynamic model, the deterministic queuing model, and discuss how the model can be adjusted and applied to different real-life scenarios. We then examine how these adjustments affect the computability, optimality, and existence of selfish routings.
We analyze the network congestion game with atomic players, asymmetric strategies, and the maximum latency among all players as social cost. This important social cost function is much less understood than the average latency. We show that the price of anarchy is at most two, when the network is a ring and the link latencies are linear. Our bound is tight. This is the first sharp bound for the maximum latency objective.
Selfish routing is a central problem in algorithmic game theory, with one of the principal applications being that of routing in road networks. Inspired by the emergence of routing technologies and autonomous driving, we revisit selfish routing and consider three possible outcomes of it: (i) $θ$-Positive Nash Equilibrium flow, where every path that has non-zero flow on all of its edges has cost no greater than $θ$ times the cost of any other path, (ii) $θ$-Used Nash Equilibrium flow, where every used path that appears in the path flow decomposition has cost no greater than $θ$ times the cost o…
School of Mathematics and Statistics, Northwestern Polytechnical University（西北工业大学数学与统计学院）；Department of Applied Mathematics, University of Twente（特温特大学应用数学系）
We study a pricing game in multi-hop relay networks where nodes price their services and route their traffic selfishly and strategically. In this game, each node (1) announces pricing functions which specify the payments it demands from its respective customers depending on the amount of traffic they route to it and (2) allocates the total traffic it receives to its service providers. The profit of a node is the difference between the revenue earned from servicing others and the cost of using others' services. We show that the socially optimal routing of such a game can always be induced by an…
The Internet is a loose amalgamation of independent service providers acting in their own self-interest. We examine the implications of this economic reality on peering relationships. Specifically, we consider how the incentives of the providers might determine where they choose to interconnect with each other. We consider a game where two selfish network providers must establish peering points between their respective network graphs, given knowledge of traffic conditions and a nearest-exit routing policy for out-going traffic, as well as costs based on congestion and peering connectivity. We …
Traditional selfish routing literature quantifies inefficiency in transportation systems with single-attribute costs using price-of-anarchy (PoA), and provides various technical approaches (e.g. marginal cost pricing) to improve PoA of the overall network. Unfortunately, practical transportation systems have dynamic, multi-attribute costs and the state-of-the-art technical approaches proposed in the literature are infeasible for practical deployment. In this paper, we offer a paradigm shift to selfish routing via characterizing idiosyncratic, multi-attribute costs at boundedly-rational travele…
Traffic congestion games abstract away from the costs of junctions in transport networks, yet, in urban environments, these often impact journey times significantly. In this paper we equip congestion games with traffic lights, modelled as junction-based waiting cycles, therefore enabling more realistic route planning strategies. Using the SUMO simulator, we show that our modelling choices coincide with realistic routing behaviours, in particular, that drivers' decisions about route choices are based on the proportion of red light time for their direction of travel. Drawing upon the experimenta…
Routing games are one of the most successful domains of application of game theory. It is well understood that simple dynamics converge to equilibria, whose performance is nearly optimal regardless of the size of the network or the number of agents. These strong theoretical assertions prompt a natural question: How well do these pen-and-paper calculations agree with the reality of everyday traffic routing? We focus on a semantically rich dataset from Singapore's National Science Experiment that captures detailed information about the daily behavior of thousands of Singaporean students. Using t…
Selfish behaviors are common in self-organized Mobile Ad hoc Networks (MANETs) where nodes belong to different authorities. Since cooperation of nodes is essential for routing protocols, various methods have been proposed to stimulate cooperation among selfish nodes. In order to provide sufficient incentives, most of these methods pay nodes a premium over their actual costs of participation. However, they lead to considerably large overpayments. Moreover, existing methods ignore mobility of nodes, for simplicity. However, owing to the mobile nature of MANETs, this assumption seems unrealistic.…
Internet and graphs are very much related. The graphical structure of internet has been studied extensively to provide efficient solutions to routing and other problems. But most of these studies assume a central authority which controls and manages the internet. In the recent years game theoretic models have been proposed which do not require a central authority and the users are assumed to be routing their flows selfishly. The existence of Nash Equilibria, congestion and the amount of inefficiency caused by this selfish routing is a major concern in this field. A type of paradox in the selfi…
We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price…
We consider a nonatomic selfish routing model with independent stochastic travel times, represented by mean and variance latency functions for each edge that depend on their flows. In an effort to decouple the effect of risk-averse player preferences from selfish behavior on the degradation of system performance, Nikolova and Stier- Moses [16] defined the concept of the price of risk aversion as the worst-case ratio of the cost of an equilibrium with risk-averse players and that of an equilibrium with risk-neutral users. For risk-averse users who seek to minimize the mean plus variance of trav…
We seek to understand when heterogeneity in user preferences yields improved outcomes in terms of overall cost. That this might be hoped for is based on the common belief that diversity is advantageous in many settings. We investigate this in the context of routing. Our main result is a sharp characterization of the network settings in which diversity always helps, versus those in which it is sometimes harmful. Specifically, we consider routing games, where diversity arises in the way that users trade-off two criteria (such as time and money, or, in the case of stochastic delays, expectation a…
This paper examines the behavior of the price of anarchy as a function of the traffic inflow in nonatomic congestion games with multiple origin-destination (O/D) pairs. Empirical studies in real-world networks show that the price of anarchy is close to 1 in both light and heavy traffic, thus raising the question: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain a positive distance away from 1 for all values of the traffic inflow, even in simple three-link networks with a single O/D pair and smooth, convex costs. …
Recent research in the social sciences has identified situations in which small changes in the way that information is provided to consumers can have large aggregate effects on behavior. This has been promoted in popular media in areas of public health and wellness, but its application to other areas has not been broadly studied. This paper presents a simple model which expresses the effect of providing commuters with carefully-curated information regarding aggregate traffic "slowdowns" on the various roads in a transportation network. Much of the work on providing information to commuters foc…
Considering congestion games with uncertain delays, we compute the inefficiency introduced in network routing by risk-averse agents. At equilibrium, agents may select paths that do not minimize the expected latency so as to obtain lower variability. A social planner, who is likely to be more risk neutral than agents because it operates at a longer time-scale, quantifies social cost with the total expected delay along routes. From that perspective, agents may make suboptimal decisions that degrade long-term quality. We define the {\em price of risk aversion} (PRA) as the worst-case ratio of the…
As autonomous cars are becoming tangible technologies, road networks will soon be shared by human-driven and autonomous cars. However, humans normally act selfishly which may result in network inefficiencies. In this work, we study increasing the efficiency of mixed-autonomy traffic networks by routing autonomous cars altruistically. We consider a Stackelberg routing setting where a central planner can route autonomous cars in the favor of society such that when human-driven cars react and select their routes selfishly, the overall system efficiency is increased. We develop a Stackelberg routi…
We study a routing game in which one of the players unilaterally acts altruistically by taking into consideration the latency cost of other players as well as his own. By not playing selfishly, a player can not only improve the other players' equilibrium utility but also improve his own equilibrium utility. To quantify the effect, we define a metric called the Value of Unilateral Altruism (VoU) to be the ratio of the equilibrium utility of the altruistic user to the equilibrium utility he would have received in Nash equilibrium if he were selfish. We show by example that the VoU, in a game wit…
We investigate traffic routing both from the perspective of theory as well as real world data. First, we introduce a new type of games: $θ$-free flow games. Here, commuters only consider, in their strategy sets, paths whose free-flow costs (informally their lengths) are within a small multiplicative $(1+θ)$ constant of the optimal free-flow cost path connecting their source and destination, where $θ\geq0$. We provide an exhaustive analysis of tight bounds on PoA($θ$) for arbitrary classes of cost functions, both in the case of general congestion/routing games as well as in the special case of …
Among the many functions a Smart City must support, transportation dominates in terms of resource consumption, strain on the environment, and frustration of its citizens. We study transportation networks under two different routing policies, the commonly assumed selfish user-centric routing policy and a socially-optimal system-centric one. We consider a performance metric of efficiency - the Price of Anarchy (PoA) - defined as the ratio of the total travel latency cost under selfish routing over the corresponding quantity under socially-optimal routing. We develop a data-driven approach to est…
Today mobile users are intensively interconnected thanks to the emerging mobile social networks, where they share location-based information with each other when traveling on different routes and visit different areas of the city. In our model the information collected is aggregated over all users' trips and made publicly available as a public good. Due to information overlap, the total useful content amount increases with the diversity in path choices made by the users, and it is crucial to motivate selfish users to choose different paths despite the potentially higher costs associated with t…
When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games, where all vehicle contribute identically to congestion. However, with the proliferation of autonomous vehicles and driver-assistance technology, vehicles become heterogeneous in how they contribute to road latency. This magnifies the potential inefficiencies due to selfish routing and invalidates traditional tolling methods. To address this, we consider a netwo…
Caching networks can reduce the routing costs of accessing contents by caching contents closer to users. However, cache nodes may belong to different entities and behave selfishly to maximize their own benefits, which often lead to performance degradation for the overall network. While there has been extensive literature on allocating contents to caches to maximize the social welfare, the analysis of selfish caching behaviors remains largely unexplored. In this paper, we model the selfish behaviors of cache nodes as selfish caching games on arbitrary directed graphs with heterogeneous content …
With energy-efficient resource allocation, mobile users and base station have different objectives. While the base station strives for an energy-efficient operation of the complete cell, each user aims to maximize its own data rate. To obtain this individual benefit, users may selfishly adjust their Channel State Information (CSI) reports, reducing the cell's energy efficiency. To analyze this conflict of interest, we formalize energy-efficient power allocation as a utility maximization problem and present a simple algorithm that performs close to the optimum. By formulating selfish CSI report…
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 ne…
We introduce a unifying model to study the impact of worst-case latency deviations in non-atomic selfish routing games. In our model, latencies are subject to (bounded) deviations which are taken into account by the players. The quality deterioration caused by such deviations is assessed by the $\textit{Deviation Ratio}$, i.e., the worst-case ratio of the cost of a Nash flow with respect to deviated latencies and the cost of a Nash flow with respect to the unaltered latencies. This notion is inspired by the $\textit{Price of Risk Aversion}$ recently studied by Nikolova and Stier-Moses. Here we…
During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our mo…
We develop a computationally efficient technique to solve a fairly general distributed service provision problem with selfish users and imperfect information. In particular, in a context in which the service capacity of the existing infrastructure can be partially adapted to the user load by activating just some of the service units, we aim at finding the configuration of active service units that achieves the best trade-off between maintenance (e.g.\ energetic) costs for the provider and user satisfaction. The core of our technique resides in the implementation of a belief-propagation (BP) al…
In congestion games, users make myopic routing decisions to jam each other, and the social planner with the full information designs mechanisms on information or payment side to regulate. However, it is difficult to obtain time-varying traffic conditions, and emerging crowdsourcing platforms (e.g., Waze and Google Maps) provide a convenient way for mobile users travelling on the paths to learn and share the traffic conditions over time. When congestion games meet mobile crowdsourcing, it is critical to incentive selfish users to change their myopic routing policy and reach the best exploitatio…
In routing games, the network performance at equilibrium can be significantly improved if we remove some edges from the network. This counterintuitive fact, widely known as Braess's paradox, gives rise to the (selfish) network design problem, where we seek to recognize routing games suffering from the paradox, and to improve the equilibrium performance by edge removal. In this work, we investigate the computational complexity and the approximability of the network design problem for non-atomic bottleneck routing games, where the individual cost of each player is the bottleneck cost of her path…
Interactions among selfish users sharing a common transmission channel can be modeled as a non-cooperative game using the game theory framework. When selfish users choose their transmission probabilities independently without any coordination mechanism, Nash equilibria usually result in a network collapse. We propose a methodology that transforms the non-cooperative game into a Stackelberg game. Stackelberg equilibria of the Stackelberg game can overcome the deficiency of the Nash equilibria of the original game. A particular type of Stackelberg intervention is constructed to show that any pos…
Two important metrics for measuring the quality of routing paths are the maximum edge congestion $C$ and maximum path length $D$. Here, we study bicriteria in routing games where each player $i$ selfishly selects a path that simultaneously minimizes its maximum edge congestion $C_i$ and path length $D_i$. We study the stability and price of anarchy of two bicriteria games: - {\em Max games}, where the social cost is $\max(C,D)$ and the player cost is $\max(C_i, D_i)$. We prove that max games are stable and convergent under best-response dynamics, and that the price of anarchy is bounded above …
This paper analyzes the behavior of selfish transmitters under imperfect location information. The scenario considered is that of a wireless network consisting of selfish nodes that are randomly distributed over the network domain according to a known probability distribution, and that are interested in communicating with a common sink node using common radio resources. In this scenario, the wireless nodes do not know the exact locations of their competitors but rather have belief distributions about these locations. Firstly, properties of the packet success probability curve as a function of …
In daily life, subjects often face a social dilemma in two stages. In Stage 1, they recognize the social dilemma structure of the decision problem at hand (a tension between personal interest and collective interest); in Stage 2, they have to choose between gathering additional information to learn the exact payoffs corresponding to each of the two options or making a choice without looking at the payoffs. While previous theoretical research suggests that the mere act of considering one's strategic options in a social dilemma will be met with distrust, no experimental study has tested this hyp…
In the classical framework of local distributed network computing, it is generally assumed that the entities executing distributed algorithms are altruistic. However, in various scenarios, the value of the output produced by an entity may have a tremendous impact on its future. This is for instance the case of tasks such as computing maximal independent sets (MIS) in networks. Indeed, a node belonging to the MIS may be later asked more than to a node not in the MIS, e.g., because MIS in networks are often used as backbones to collect, transfer, and broadcast information, which is costly. In th…
Algorithmic graph theory has thoroughly analyzed how, given a network describing constraints between various nodes, groups can be formed among these so that the resulting configuration optimizes a \emph{global} metric. In contrast, for various social and economic networks, groups are formed \emph{de facto} by the choices of selfish players. A fundamental problem in this setting is the existence and convergence to a \emph{self-enforcing} configuration: assignment of players into groups such that no player has an incentive to move into another group than hers. Motivated by information sharing on…
How can a system designer exploit system-level knowledge to derive incentives to optimally influence social behavior? The literature on network routing contains many results studying the application of monetary tolls to influence behavior and improve the efficiency of self-interested network traffic routing. These results typically fall into two categories: (1) optimal tolls which incentivize socially-optimal behavior for a known realization of the network and population, or (2) robust tolls which provably reduce congestion given uncertainty regarding networks and user types, but may fail to o…
We study a routing game in an environment with multiple heterogeneous information systems and an uncertain state that affects edge costs of a congested network. Each information system sends a noisy signal about the state to its subscribed traveler population. Travelers make route choices based on their private beliefs about the state and other populations' signals. The question then arises, "How does the presence of asymmetric and incomplete information affect the travelers' equilibrium route choices and costs?'' We develop a systematic approach to characterize the equilibrium structure, and …
This paper studies an interference interaction (game) between selfish and independent wireless communication systems in the same frequency band. Each system (player) has incomplete information about the other player's channel conditions. A trivial Nash equilibrium point in this game is where players mutually full spread (FS) their transmit spectrum and interfere with each other. This point may lead to poor spectrum utilization from a global network point of view and even for each user individually. In this paper, we provide a closed form expression for a non pure-FS epsilon-Nash equilibrium po…
Hebrew University（希伯来大学）；Microsoft Research Israel（微软研究院以色列分院）；Technion（以色列理工学院）
Information delivery in a network of agents is a key issue for large, complex systems that need to do so in a predictable, efficient manner. The delivery of information in such multi-agent systems is typically implemented through routing protocols that determine how information flows through the network. Different routing protocols exist each with its own benefits, but it is generally unclear which properties can be successfully combined within a given algorithm. We approach this problem from the axiomatic point of view, i.e., we try to establish what are the properties we would seek to see in…
In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish users and cooperative users, respectively. Based on the utility definition for cooperative users, we show that the channel allocation problem can be formulated as a potential game, and thus converges to a deterministic channel allocation Nash equilibrium point. Alternatively, a no-regret learning implementation is proposed for both scenarios an…
Social networks offer users new means of accessing information, essentially relying on "social filtering", i.e. propagation and filtering of information by social contacts. The sheer amount of data flowing in these networks, combined with the limited budget of attention of each user, makes it difficult to ensure that social filtering brings relevant content to the interested users. Our motivation in this paper is to measure to what extent self-organization of the social network results in efficient social filtering. To this end we introduce flow games, a simple abstraction that models network …
