Selfish Users Research Articles

Gather or Scatter: Stackelberg-Game-Based Task Decision for Blockchain-Assisted Socially Aware Crowdsensing Framework

Mobile Crowdsensing (MC), an excellent solution to large-scale spatio-temporal data sensing problems, has recently received lots of attention from both industry and academia. In the MC system, any requester can acquire the sensing data for his points of interest (PoIs) by offering some payments to attract a group of mobile users capable of completing these PoI-related sensing tasks. However, the current MC work neglected three vital factors, more or less. First, they assume that these distributed users are mutually independent in MC, ignoring the social effects. Actually, the sensing data collected by one user may be corroborated by others’ sensing data, so-called “information corroboration”. Second, all rational and selfish users are inclined to gather to perform these tasks due to information corroboration. Meanwhile, they may be strategic about their participation levels to maximize profits. However, more similar sensing data will undoubtedly lower the information value, so any user has a tradeoff between gather and scatter. Third, although mobile users can obtain some payments, privacy issues may still prevent them from participating in MC. In this paper, we propose a secure blockchain-assisted socially-aware MC framework by adopting the smart contract technique of Ethereum. For this framework, we further devise a two-stage Stackelberg game model to assist the requester (i.e., the leader in the game) in properly pricing each PoI-related sensing task, so that mobile users (i.e., the followers in the game) can exactly select their tasks and determine their participation levels. To analyze the game equilibrium, we extend the traditional Hessian matrix method to a multi-dimension case involving the multi-user multi-task hyperspace setting. We conduct extensive experiments to prove the equilibrium and effectiveness of the proposed solution. We also implement a prototype and deploy the smart contract to an official Ethereum test network to demonstrate the practicability of the proposed framework.

When Congestion Games Meet Mobile Crowdsourcing: Selective Information Disclosure

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 exploitation-exploration trade-off. By considering a simple but fundamental parallel routing network with one deterministic path and multiple stochastic paths for atomic users, we prove that the myopic routing policy's price of anarchy (PoA) can be arbitrarily large as the discount factor approaches 1. To remedy such huge efficiency loss, we propose a selective information disclosure (SID) mechanism: we only reveal the latest traffic information to users when they intend to over-explore the stochastic paths, while hiding such information when they want to under-explore. We prove that our mechanism reduces PoA to less than 2. Besides the worst-case performance, we further examine our mechanism's average-case performance by using extensive simulations.

Selfish-Aware and Learning-Aided Computation Offloading for Edge–Cloud Collaboration Network

Mobile edge computing (MEC) raises the problem of selfish user devices that utilize less computing resources than expected to execute offloading tasks or maliciously discard computation tasks. However, most of the existing work either focused on the task offloading or concentrated on the trust mechanism in MEC systems. By jointly considering the two challenges, in this paper, we propose a selfish-aware and learning-aided computation offloading scheme for edge-cloud collaboration network. Specifically, we first design a selfishness evaluation mechanism to evaluate the selfishness of the user devices based on the historical interaction records of the edge-cloud collaboration network. Then, we construct the task offloading model which introduces the selfishness evaluation mechanism to suppress the selfish user devices. On this basis, we further formalize the selfish-aware task offloading as an optimization problem of the weighted sum of time latency and energy consumption. Thereafter, we take one step further formalizing the optimization problem as a Markov Decision Process (MDP), and design a task offloading algorithm based on deep reinforcement learning (DRL) to find the optimized task offloading decision. The simulation results demonstrate that our work can decrease the time latency and energy consumption as well as suppress the selfish user devices.

Blockchain based smart contract for cooperative spectrum sensing in cognitive radio networks for sustainable beyond 5G wireless communication

Cognitive radio networks allow opportunistic spectrum access to the unlicensed users, which rely on effective spectrum sensing. Recently, cooperative sensing has been found to improve sensing reliability. However, sometimes the selfish users do not cooperate, and therefore, different incentive design mechanisms like contract theory have been proposed recently, where the cooperation is encouraged by offering appropriate reward to the sensing participants. However, still no secure structure exists for the reward distribution after a successful contract completion, and a user may also deny sensing even after accepting the contract. This work proposes the use of blockchain-based smart contracts, which are based upon a permissioned blockchain that helps in making the transactions private among the participants. Further, the efficiency of this approach is improved by introducing a reputation parameter for the users. This measures the trustworthiness of a particular user based upon the accuracy of their recent sensing results. Further, a money locking approach is proposed from which a penalty is deducted if the user denies or fails to submit a correct reading. Performance analysis of the proposed scheme is done to show the superiority of the scheme.

A Novel Stackelberg-Game-Based Energy Storage Sharing Scheme Under Demand Charge

Demand response (DR) using shared energy storage systems (ESSs) is an appealing method to save electricity bills for users under demand charge and time-of-use (TOU) price. A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study. In this scheme, the interactions between selfish users and an operator are characterized as a Stackelberg game. Operator holds a large-scale ESS that is shared among users in the form of energy transactions. It sells energy to users and sets the selling price first. It maximizes its profit through optimal pricing and ESS dispatching. Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced. This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model. The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users' costs. The bi-level model is transformed and linearized into a mixed-integer linear programming (MILP) model using the mathematical programming with equilibrium constraints (MPEC) method and model linearizing techniques. Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.

A Data-driven Pricing Scheme for Optimal Routing through Artificial Currencies

Mobility systems often suffer from a high price of anarchy due to the uncontrolled behavior of selfish users. This may result in societal costs that are significantly higher compared to what could be achieved by a centralized system-optimal controller. Monetary tolling schemes can effectively align the behavior of selfish users with the system-optimum. Yet, they inevitably discriminate the population in terms of income. Artificial currencies were recently presented as an effective alternative that can achieve the same performance, whilst guaranteeing fairness among the population. However, those studies were based on behavioral models that may differ from practical implementations. This paper presents a data-driven approach to automatically adapt artificial-currency tolls within repetitive-game settings. We first consider a parallel-arc setting whereby users commute on a daily basis from an individual origin to an individual destination, choosing a route in exchange of an artificial-currency price or reward, while accounting for the impact of the choices of the other users on travel discomfort. Second, we devise a model-based reinforcement learning controller that autonomously learns the optimal pricing policy by interacting with the proposed framework considering the closeness of the observed aggregate flows to a desired system-optimal distribution as a reward function. Our numerical results show that the proposed data-driven pricing scheme can effectively align the users’ flows with the system optimum, significantly reducing the societal costs with respect to the uncontrolled flows (by about 15% and 25% depending on the scenario), and respond to environmental changes in a robust and efficient manner.

A new framework for mixed-user dynamic traffic assignment considering delay and accessibility to information

We consider a transport network consisting of two classes of users, namely, selfish users whose objective is to minimize their individual travel times, and cooperative users whose objective is to maximize the aggregate throughput of their class, or equivalently, to minimize the total travel time of their class. The selfish users decide the paths from their respective origins to destinations depending on their knowledge of the traffic conditions prevailing up to the beginning of their journeys, and they do not alter their paths once their journeys start. The cooperative users, on the other hand, keep making the decisions of ‘the next link to take towards the destination’ throughout their journeys based on their current knowledge of the traffic conditions, which evolves with time and the availability of traffic information. We develop a new framework for the problem of informed mixed-user dynamic traffic assignment (IMUDTA) considering the delay and the degree of penetration of information. The proposed framework enables us to study the route choices made by the two classes of users and the resulting network performance. Due to its non-linear formulation with high complexity, we propose a novel incremental solution method to this problem where we present a transformation of this complex IMUDTA problem into a relaxed linear programming (LP) model. We show via numerical results that (i) appropriately postponing (intentionally or unintentionally) the access to information can improve the system performance, (ii) better information penetration increases the robustness of the network performance against the information delay, and (iii) the value of information (in terms of improving network performance) is reduced when the degree of information penetration is high. The applicability of our framework is demonstrated in a large-scale network example, and analyze the computational aspects and the impact of information on network performance with varying information delay and penetration.

Truthful auction mechanisms for VNF chain provisioning and allocation across geo-distributed datacenters

With the fast development of network function virtualization (NFV), NFV markets are emerging that allows network service providers (NSPs) to trade different virtual network function (VNF) chains among users. Therefore, efficient mechanisms for VNF chain provisioning and allocation are key to guarantee efficient operations of the NFV markets. One fundamental issue is how to maximize the social welfare of the market such that selfish users have incentives to acquire VNF chains from the markets. To overcome this issue, in this paper, we propose a truthful randomized combinatorial auction mechanism (TRCAM), which integrates the primal–dual approximation algorithm design technique and efficient pricing strategy. This mechanism considers dynamic VNF chain provisioning of the NSP and flexible VNF chain deployment of users. To be specific, we first formulate the social welfare maximization problem as an integer linear program, which is proven to be NP-hard. Then, we propose a primal–dual approximate algorithm which is near-optimal with polynomial-time complexity and employ it as a building block to design the TRCAM. Furthermore, we develop a novel binary-search-based algorithm to boost the average-case performance of the TRCAM. Both strict theoretical analysis and extensive experimental studies demonstrate the effectiveness of our proposed TRCAM, which achieves approximate truthfulness, near-optimal social welfare, individual rationality, and computational efficiency.

An Anti-Jamming Multiple Access Channel Game Using Latency as Metric

We consider a multi-access channel problem, where several selfish users communicate with a base station (BS) in the presence of a jammer. The jammer wishes to degrade the communication by producing interference. The communication metric is the inverse signal-to-interference-plus-noise ratio (SINR), which, for low SINR, reflects communication delay. The problem is formulated in Nash and Stackelberg game frameworks. The equilibrium is derived in closed form for both models. The usability of the latency metric even in the presence of a jammer is proven by showing that the equilibrium is unique.

A low-cost communication security scheme of UAV based on multi-round reverse auction model

In recent years, the security of wireless communication has received more and more attention. However, with the increasing requirements for security performance in the process of wireless communication, the cost of improving security also increases. Therefore, how to improve the security of wireless communication while reducing costs has become a serious challenge. Aiming at the security problems in the UAV-assisted wireless communication link based on the premise of low cost and high profit, this paper studies how to motivate non-offloading users to send jamming power to interfere with eavesdropping UAVs, so efficiently and economically to improve the security performance of wireless communication link. Firstly, the relationship between the security performance of the communication link and the interference power is revealed through the theoretical model. Then, we propose a scenario consisting of a legitimate UAV, a ground user group, and an eavesdrop UAV. In this scenario, we divide the ground users into offloading users and non-offloading users. At the same time, the cost functions for offloading users and utility functions for non-offloading users are defined, and non-offloading users are encouraged to help to offload users unload data safely to a legitimate UAV by obtaining rewards for offloading users. Considering the selfishness of users, a reverse auction algorithm based on multi-user groups is proposed to achieve the optimal mapping between non-offloading users and offloading users. Finally, the effectiveness of the proposed scheme is verified by a large number of simulations. The research results show that the scheme innovative designs a method for users to cooperate to interfere with eavesdroppers, which can reduce costs and improve utility while maximizing the improvement of wireless communication link security.

Enhanced Reputation-based Tit-for-Tat Strategy for Collaborative Social Applications

Social applications have witnessed a rapid growth in their use. Millions of people are utilizing them on a daily basis in order to share their experience, information and to communicate with their family members and friends. Lately, these technologies have been used to foster collaboration in education, however, it is a case of hit and miss and without established techniques to ensure or replicate success. One known problem that can impact the sustainability of collaborative social applications is the presence of selfish users. A selfish user adopts a free riding behaviour that takes advantage of the collaborative group without contributing back which would affect the group’s survivability. However, the inability to contribute back is not necessarily due to selfishness. In fact, cooperative learners may avoid participating due to the lack of expertise and/or confidence. In the literature, repeated non-cooperative game theory was introduced as a solution where several strategies were introduced to identify selfish users. However, such strategies do not differentiate between selfish learners and cooperative learners who are reluctant to answer others’ requests either due to lack of knowledge or confidence. In this paper, we show that educational and collaborative groups need to distinguish between those types of users and put in place mechanisms to encourage non contributing cooperative learners to participate rather than punishing them and excluding them from the group. An enhanced reputation-based Tit-for-Tat strategy is proposed as a solution that will enhance the group activity and overall gain.

Run for Your Life

Run for Your Life Kim McLarin (bio) In the years after my divorce I underwent a prolonged emotional crisis, one which involved bouts of depression, great batches of French fries, and a stubborn habit of falling in love with men who did not love me in return. For the most part these men were not bad people, were not, as they hacked their way through the swamp of midlife dating, deliberately destructive, or at least no more so than I. There was, however, one person whose bad behavior was intentional, who was—in his dealings with women in general and me in particular—selfishly, gleefully, actively unkind. This person reveled in the notion of having an upper hand in relationships, of power as aphrodisiac. Alternately attentive and dismissive, lying and truthful, nastily disparaging and lavish with praise, he kept me off-center and I allowed it, drawn to the treatment like a cat towards catnip. Catnip sprinkled on coals. It was a messy, painful, damaging connection, not good for anyone. My friends, watching from the sidelines, frequently registered their concern and disapproval, but I remained unhearing and unmoved. Eventually one said, “You know, this is an abusive relationship.” I bristled. An abusive relationship? The summation rankled. The man in question had never hit me, never become physical, never so much as threatened violence. Yes, he was a jerk, a selfish user without remorse. But an abuser? Wouldn’t that make me a victim? Wouldn’t that make me weak? The definition of abuse is this: to use wrongly or improperly, use to bad effect or for a bad purpose, to misuse; to hurt or injure by maltreatment; to treat a person or animal with cruelty or violence. Not all of these things were true about the relationship, but a few of them were. Enough to fail to ease my discomfort. Enough to make me think. If the situation was not precisely abusive, it was certainly dys-functional, and the primary distinction, I came to realize, was the issue of power. In my case, the only power this guy had over me was power I handed to him. In summer 2020, after police officers in Wisconsin shot Jacob Blake in the back seven times as he leaned into the car where his children sat, I came across a video clip on the internet. It wasn’t the shooting; I have not watched a video of police shooting or ramming or kneeling on the necks of Black people since Rodney King. The clip I stumbled across was an interview with Doc Rivers, coach [End Page 146] of the Los Angeles Clippers. He sat on a bench after some game, discussing not fouls and shots but the police shooting of Mr. Blake and other Black people, the cynical fear-mongering of then-President Donald Trump and other Republicans, the way peaceful Black protest is met with force while violent white protest is met with shrugs. Forcing back tears, Coach Rivers said: “It’s amazing why we keep loving this country and this country doesn’t love us back.” Well, there you go, I thought. That is an abusive relationship. _______ According to the National Coalition Against Domestic Violence, a person experiencing abuse may be embarrassed or fear judgment and stigmatization; love the person who is abusing them and believe that they will change; deny that anything is wrong; and/or excuse the other person. The person may also behave in ways that can be difficult for people outside the relationship to understand. These behaviors include refusing to leave the relationship; believing that the other person is powerful or knows everything; idealizing the person who carried out the abuse during periods of calm; and believing the abuse is deserved. _______ When I was a child the Fourth of July passed with little fuss. Maybe my mother burned some hotdogs on our small charcoal grill, maybe my uncle brought over some sparklers and we ran around fizzling in the dark. Even the Bicentennial, which swept up the nation in a fervor of nostalgia and self-love, meant to us mostly televised fireworks and tall ships (both disappointing) and everything in the supermarket suddenly packaged...

Time-Constrained Service Handoff for Mobile Edge Computing in 5G

Many mobile device applications require low end-to-end latency to edge computing infrastructure when offloading their computation tasks in order to achieve real-time perception and cognition for users. User mobility brings significant challenges in providing low-latency offloading due to the limited coverage area of cloudlets. Virtual machine (VM)/container handoff is a promising solution to seamlessly transfer services from one cloudlet to another to maintain low latency as users move. However, an inefficient path planning for the handoff can result in system congestion and consequently poor quality of service (QoS). The situation can even worsen by selfish users who intentionally lie about their true parameters to achieve better service at the cost of degrading the whole system's performance. To fill this research gap, we propose an Online Service Handoff Mechanism (OSHM) to provide an efficient path dynamically for transferring VM/container from the current serving cloudlet to a nearby cloudlet at the destination of a mobile user. Our proposed path planning algorithm is based on a label correction methodology, leading to polynomial time complexity. OSHM is accompanied by our proposed payment determination function to discourage misreporting of unknown parameters. We discuss the theoretical properties of our proposed mechanism in implementing a system equilibrium and ensuring truthfulness. We also perform a comprehensive assessment through extensive experiments which show the efficiency of OSHM in terms of workload, handoff time, consumed energy, and other metrics compared to several benchmarks. Experimental results show that OSHM outperforms other algorithms, reducing at least 61% in average workload, 33% in average handoff time, and 29% in average energy consumption.

Incentive Mechanism and Resource Allocation for Edge-Fog Networks Driven by Multi-Dimensional Contract and Game Theories

The edge computing paradigm has become extremely popular over the past years, as a means of offloading computationally intensive tasks by users of resource and battery-constrained devices. Nevertheless, the edge networks’ overexploitation by the ever-increasing number of task-offloading users, gradually leads to their performance degradation. In this paper, we leverage on the different levels of available computing capabilities across the network, and we design an incentive mechanism that aims to shift the selfish users’ preference from the edge to the upper fog computing layer, accounting for their level of delay tolerance. To deal with the users’ heterogeneity in terms of their applications’ multi-dimensional distinctive features (including their delay tolerance/sensitivity), a multi-dimensional contract theory modeling is adopted, according to which the edge server determines the bundles of the users’ provided efforts and corresponding offered rewards. In this respect, each user’s effort represents the amount of its initially offloaded task at the edge that is allowed to be further forwarded and processed at the fog. Considering that the users-to-edge server offloading is performed under Non-Orthogonal Multiple Access (NOMA), the problem of joint computation task offloading and uplink transmission power allocation is subsequently addressed via a Stackelberg game, where the edge server and the users are treated as leader and followers, respectively. The aim of the game is to minimize the end-to-end network’s energy consumption and increase its resource utilization efficiency. The incentive mechanism and resource allocation framework is evaluated via modeling and simulation regarding its operation and efficiency under different scenarios.

Optimal Pricing for Job Offloading in the MEC System With Two Priority Classes

Multi-Access edge computing (MEC) is an emerging paradigm where users offload computationally intensive jobs to the Access Point (AP). Given that the AP's resources are shared by selfish users, pricing is a useful tool for incentivising users to internalize the negative externality of delay they cause to other users. Nevertheless, different users have different negative valuations towards delay as some are more delay sensitive. To serve heterogeneous users, we propose a priority pricing scheme where users can get served first for a higher price. Our goal is to find the prices such that in decision making, users will choose the class and the offloading frequency that jointly maximize social welfare. With the assumption that the AP knows users' profit functions, we derive in semi-closed form the optimal prices. However in practice, the reporting of users's profit information incurs a large signalling overhead. Besides, in reality users might falsely report their private profit information. To overcome this, we further propose a partial-knowledge based pricing mechanism where no knowledge of individual user profit functions is required. At equilibrium, the optimal prices and average edge delays are learnt, and users have chosen the correct priority class and offload at the socially optimal frequency.

Optimal Target User Selection Policy for D2D Wireless Caching Networks

Device-to-device (D2D) communication is one of the core technologies of 5 G and can mitigate the scarcity of spectrum resources for wireless communication systems because it involves direct communication from device to device. However, the instability of the network environment, the explosion in the number of users, the variability of user locations and the existence of selfish users increase the time required to search for target users and data transmission delay. In this paper, an optimal target user local search (OTULS) algorithm with blockchain technology is proposed to reduce the time delay in searching for a target user and the data transmission delay between devices. We shift the target cache users search task from the local area to the base station by the OTULS. Based on the target cache users, we search for the target user with the shortest distance from the requester at local. In addition, to avoid selecting selfish users with the shortest distance from the target cache users, we manage the users’ reputations through a blockchain. The proposed algorithm can reduce the delay in the target user search and in data transmission compared with other algorithms.

Collaborative Edge Computing for Social Internet of Vehicles to Alleviate Traffic Congestion

Edge computing in vehicles is emerging as an essential candidate for the Internet of Vehicles (IoV) to improve traffic efficiency. The proliferation of IoV pushes the horizon of edge computing. The social features and connections among vehicles are significant for traffic efficiency solutions. However, it is quite challenging to perform collaborative edge computing (CEC) for social IoV systems because of network heterogeneity, vehicle mobility, user selfishness, privacy, and so on. This article focuses on the CEC, in the social IoV system to alleviate urban traffic congestion. Recent research reveals that intelligent traffic lights control through city-wide mobile edge computing (MEC) servers can reduce vehicles’ average waiting time at signal intersections. This article has focused on a CEC-based traffic management system (CEC-TMS) to reduce the average waiting time. It utilizes multiagent-based deep reinforcement learning (DRL) for the MEC servers that interact with IoV and traffic lights to generate dynamic green waves at congested intersections. Results demonstrate the effectiveness of the proposed system under the paradigm of multiagent DRL.

Strategy-Proof Online Mechanisms for Weighted AoI Minimization in Edge Computing

Real-time information processing is critical to the success of diverse applications from many areas. Age of Information (AoI), as a new metric, has received considerable attention to evaluate the performance of real-time information processing systems. In recent years, edge computing is becoming an efficient paradigm to reduce the AoI and to provide the real-time services. Considering the substantial deployment cost and the resulting resource limitation in edge computing, a proper pricing mechanism is highly necessary to fully utilize edge resources and then minimize the overall AoI of the whole system. However, there are two challenges to design this mechanism: 1) the priorities (or values) of the real-time computing tasks, critical to the efficient resource allocation, are usually private information of users and may be manipulated by selfish users for their own interests; 2) due to the time-varying property of AoI, the values of the tasks discount with time, making the traditional pricing mechanisms infeasible. In this paper, we extend the classical Myerson Theorem to the online setting with time discounting tasks values, and accordingly propose an online auction mechanism, called PreDisc, including an allocation rule and a payment rule. We leverage dynamic programming to greedily allocate resources in each time slot, and charge the winning user with a new critical price, extended from the classical Myerson payment rule. A preemption factor is further employed to make a trade-off between the newly arrived tasks and ongoing tasks. We prove that PreDisc guarantees the economic property of strategy-proofness and achieves a constant competitive ratio. We conduct extensive simulations and the results demonstrate that PreDisc outperforms the traditional mechanisms, in terms of both weighted AoI and revenue of edge service providers. Compared with the optimal solution in offline VCG mechanism, PreDisc has much lower computation complexity with only a slight performance loss.

Futility of being selfish in optimized traffic.

Optimizing traffic flow is essential for easing congestion. However, even when globally optimal, coordinated, and individualized routes are provided, users may choose alternative routes which offer lower individual costs. By analyzing the impact of selfish route choices on performance using the cavity method, we find that a small ratio of selfish route choices improves the global performance of uncoordinated transportation networks but degrades the efficiency of optimized systems. Remarkably, compliant users always gain in the former and selfish users may gain in the latter, under some parameter conditions. The theoretical results are in good agreement with large-scale simulations. Iterative route switching by a small fraction of selfish users leads to Nash equilibria close to the globally optimal routing solution. Our theoretical framework also generalizes the use of the cavity method, originally developed for the study of equilibrium states, to analyze iterative game-theoretical problems. These results shed light on the feasibility of easing congestion by route coordination when not all vehicles follow the coordinated routes.

Pricing of Connected and Autonomous Vehicles in Mixed-Traffic Networks

For networks with human-driven vehicles (HDVs) only, pricing with arc-specific tolls has been proposed to achieve minimization of travel times in a decentralized way. However, the policy is hardly feasible from a technical viewpoint without connectivity. Therefore, for networks with mixed traffic of HDVs and connected and autonomous vehicles (CAVs), this paper considers pricing in a scenario where only CAVs are charged. In contrast to HDVs, CAVs can be managed as individual vehicles or as a fleet. In the latter case, CAVs can be routed to minimize the travel time of the fleet of CAVs or that of the entire fleet of HDVs and CAVs. We have a selfish user behavior in the first case, a private monopolist behavior in the second, a social planner behavior in the third. Pricing achieves in a decentralized way the social planner optimum. Tolls are not unique and can take both positive and negative values. Marginal cost pricing is one solution. The valid toll set is provided, and tolls are then computed according to two schemes: one with positive tolls only and minimum toll expenditure, and one with both tolls and subsidies and zero net expenditure. Convergent algorithms are used for the mixed-behavior equilibrium (simplicial decomposition algorithm) and toll determination (cutting plane algorithm). The computational experience with three networks: a two-arc network representative of the classic town bypass case, the Nguyen-Dupuis network, and the Anaheim network, provides useful policy insight.