Optimal Social Welfare Research Articles

Online Multi-Resource Social Welfare Maximization for Non-Preemptive Jobs

Multi-resource allocation is ubiquitous in datacenters. Usually, the datacenter scheduler associates each user with a utility function and then allocates multiple resources so as to maximize the social welfare, which is the sum of the utilities of the users. We refer to this problem as the Social Welfare Maximization (SWM) problem. Meanwhile, given the dynamic nature of datacenters, the scheduler is supposed to support non-preemptive scheduling, where jobs of users that are being processed would not be interrupted by the reconfiguration of resources. Non-preemptive solutions to SWM incorporating pricing considerations include dynamic pricing and bidding/auctions. However, both strategies are quite complex. Meanwhile, traditional Lagrange solutions to SWM does not support non-preemptive job scheduling. In this paper, we propose Adaptive Dominant Resource Fairness (ADRF), that provides near-optimal social welfare where each user is assigned an α-fair utility function and when 1 <; α ≤ 2. Based on ADRF, we propose Cumulative ADRF (C-ADRF), an online algorithm that greedily assigns the idle resources to the current poorest user, making it quite simple to schedule jobs from users non-preemptively. Compared with the polynomial or exponential form of time complexities in other SWM solutions, C-ADRF requires only O(log N) work, where N is the number of users. Extensive simulations using Google and Facebook cluster-data traces show an impressive behavior of C-ADRF in providing social welfare, only 3% and 2% away from the optimal social welfare, respectively.

Managing Influenza Vaccination: The Role of Bounded Rationality

Problem Definition: Under the assumption of full rationality, the existing literature shows that self-interested individuals ignore the social benefit of protecting others when making influenza vaccination decisions (positive externality), which results in social welfare loss. In this paper, we study the impact of individual bounded rationality in influenza vaccination settings. Academic/Practical Relevance: We examine the commonly used vaccination policies in practice such as subsidization and taxation and provide managerial guidelines for a social planner. Methodology: We develop a simple game-theoretic model, in which individuals boundedly rationally estimate the vaccinated fraction of the population through anecdotal reasoning. We characterize individuals' optimal vaccination decisions and the social planner's optimal subsidization and taxation policies. Results: We find that individual bounded rationality may lead to a positive externality improving social welfare. When the zero-risk vaccination fraction is low and the vaccination cost is at a particular level, the negative effect of self-interested individuals' vaccination decisions could be completely eliminated because of bounded rationality and thus the socially optimal welfare is achieved. In sharp contrast to the setting of full rationality, we show that the optimal social welfare may never be achieved by any subsidization or taxation policy under individual bounded rationality. Managerial Implications: We demonstrate the welfare loss by ignoring individual bounded rationality when implementing a vaccination policy. The social planner should consider the level of individual bounded rationality when using subsidization or taxation in practice. We find that the social planner should induce a particular level of accuracy in estimating the vaccinated fraction for the individuals when the vaccination cost is sufficiently low to achieve the socially optimal welfare by subsidization or taxation; otherwise, inducing individuals to obtain more accurate estimation of the vaccinated fraction is always recommended.

Optimal Lockdown and Social Welfare

This paper reexamines the design of the optimal lockdown strategy by paying attention to its robustness to the postulated social welfare criterion. We first characterize optimal lockdown under utilitarianism, and we show that this social criterion can, under some conditions, imply a COVID19 variant of Parfit’s (1984) Repugnant Conclusion: for any non-maximal lockdown saving lives at the cost of reducing average utility at a given period, there exists always a stricter lockdown, which further reduces average utility, but leads to a larger aggregate welfare. The optimal lockdown under utilitarianism is also shown to deteriorate the situation of the worst-off, against Hammond Equity. In order to do justice to Hammond Equity, we characterize optimal lockdown under the ex post egalitarian criterion, which gives absolute priority to the worst-o¤ ex post. Under general conditions, the ex post egalitarian optimum involves a zero lockdown. Varying between zero and its maximal level, the optimal lockdown policy is not robust to the postulated ethical criterion.

Combining Microsimulation and Optimization to Identify Optimal Flexible Tax-Transfer Rules

We use a behavioural microsimulation model embedded in a numerical optimization procedure in order to identify optimal (social welfare maximizing) tax-transfer rules. We consider the class of tax-transfer rules consisting of a universal basic income and a tax defined by a 4th degree polynomial. The rule is applied to total taxable household income. A microeconometric model of household, which simulates household labour supply decisions, is embedded into a numerical routine in order to identify – within the class defined above – the tax-transfer rule that maximizes a social welfare function. We present the results for five European countries: France, Italy, Luxembourg, Spain and United Kingdom. For most values of the inequality aversion parameter, the optimized rules provide a higher social welfare than the current rule, with the exception of Luxembourg. In France, Italy and Luxembourg the optimized rules are significantly different from the current ones and are close to a Negative Income Tax or a Universal basic income with a flat tax rate. In Spain and the UK, the optimized rules are instead close to the current rule. With the exception of Spain, the optimal rules are slightly disequalizing and the social welfare gains are due to efficiency gains. Nonetheless, the poverty gap index tends to be lower under the optimized regime.

Game-Theoretic Analysis to Examine How Government Subsidy Policies Affect a Closed-Loop Supply Chain Decision

The pros and cons of government subsidy policies in a closed-loop supply chain (CLSC) setting on optimal pricing, investment decisions in improving product quality, and used product collection under social welfare (SW) optimization goal have not been examined comprehensively. This study compares the outcomes of three government policies under manufacturer-Stackelberg (MS) and retailer-Stackelberg (RS), namely (i) direct subsidy to the consumer, (ii) subsidy to the manufacturer to stimulate used product collection, and (iii) subsidy to the manufacturer to improve product quality. Results demonstrate that the greening level, used product collection, and SW are always higher under the RS game, but the rate of a subsidy granted by the government is always higher under the MS game. Profits for the CLSC members and SW are always higher if the government provides a subsidy directly to the consumer, but productivity of investment in the perspective of the manufacturer or government are less. In a second policy, the government organizations grant a subsidy to the manufacturer to stimulate used product collection, but it does not necessarily yield the desired outcome compared to others. In a third policy, the manufacturer receives a subsidy on a research and development (R&amp;D) investment, but it yields a sub-optimal greening level. This study reveals that the outcomes of subsidy policies can bring benefit to consumers and add a degree of complication for CLSC members; government organizations need to inspect carefully among attributes, mainly product type, power of CLSC members, and investment efficiency for the manufacturer, before implementing any subsidy policies so that it can lead to an environmentally and economically viable outcome.

Medicine Pricing, Optimal Patent Length and Social Welfare

Social welfare, the ultimate pursuit of medicine patent protection, is affected by multiple market and government factors. This paper constructs a multi-stage dynamic sequential game model involving the government and medicine enterprises and integrates various market and government factors into account. Next, the social welfare of monopoly pricing and government pricing are compared, while the optimal length and its correlations with the influencing factors are determined for medicine patent. It is concluded that the optimization of medicine patent length is a complex decision-making process; the optimal patent length is affected by pricing mode, government subsidy, market demand elasticity, R&D investment, marginal cost, product lifecycle and discount rate. The government should determine medicine patent length according to local conditions, rationalize medicine pricing mechanism, and develop a competitive medicine market.

Evaluating the market power and coalition formation in double-sided power market: An analytical decomposition approach

In this paper, new indices of the market power are defined to recognize and prioritize the potentials of market power as well as the feasibility of forming a profitable coalition of electricity market players. To this aim, the social welfare optimization problem is formulated and solved in a double-sided power market environment. Then, by forming the Lagrange function, Karush Kuhn Tucker (KKT) conditions are analytically developed. Three major outputs of the above problem including the Locational Marginal Price (LMP), the generation power of each unit and the dispatched elastic load of each Load Service Entity (LSE) are decomposed into basic structural factors. These factors include supply, demand and line congestion effects. Using the coefficients obtained from the structural decomposition, four profit-based market power indices are formulated: (1) profit index of each generator, or GenCo, due to the change of generation units’ bids; (2) profit index of each generator, or GenCo, due to the change of LSEs’ offers; (3) benefit index of each LSE due to the change of generation units’ bids, and (4) benefit index of each LSE due to the change of their offers. The impact of changes in a player’s bidding/offering strategy on its own profits determines the market power of that player. In addition, these changes affect other players' profits. So, the possibility of forming a profitable coalition can be evaluated. The proposed method is simulated on the IEEE 24-bus test system and the proposed indices are calculated and analyzed. Assessment results provide valuable implications for market regulators to monitor the competition level of the power market.

Fully-decentralized coordination for simultaneous hydrogen, power, and heat interaction in a multi-carrier-energy system considering private ownership

This paper focuses on a multi-agent system-based fully-decentralized coordination approach over a multi-carrier energy system comprising of thermal, electrical, and hydrogen loads. The system has a connection with up-stream electricity network. All agents in the proposed approach such as photovoltaic agent, electrolyzer agent, and fuel cell agent are active in thermal, electrical, and hydrogen interactions, influencing the clearing price of those simultaneous interactions. Furthermore, in this cooperative model, each agent has a private ownership; thus, in addition to social welfare optimization, each agent also tries to maximize its own profit via communication with the rest of agents. Since all agents try to satisfy the power balance constraint and their own local constraints through this communication, the need for a central agent is obviated for the balance of power. To evaluate the proposed multi-agent-based model, simulations were carried out in ‘Any Logic.’ Then, the effect of load-shedding by demand response program in simultaneous thermal, electrical, and hydrogen interactions of multi-carrier energy system was investigated. Finally, the obtained simulation results of the proposed decentralized model were compared with those of the centralized model. The obtained results demonstrated the validity of the proposed model.

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices under a range of assumptions about the designer’s information and agents’ valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with subadditive valuations over identical items, even in an incomplete-information setting and with uniform prices. We also show that no constant-factor guarantee is possible for general valuations over identical items, even in a full-information setting and with non-uniform prices.

Non-Cooperative and Cooperative Optimization of Scheduling With Vehicle-to-Grid Regulation Services

Due to the increasing popularity of electric vehicles (EVs) and technological advancements of EV electronics, the vehicle-to-grid (V2G) technique, which utilizes EVs to provide ancillary services for the power grid, stimulates new ideas in current smart grid research. Since EVs are selfish individuals owned by different parties, how to motivate them to provide ancillary services becomes an issue. In this paper, game theoretic approaches using non-cooperative and cooperative game are proposed to motivate EVs to provide frequency regulation services for the power grid. In a non-cooperative V2G system, the interaction between the EV aggregator and EVs is formulated as a non-cooperative Stackelberg game. The EV aggregator as the leader decides the electricity trading price, and EVs as the followers determine their charging/discharging strategies. In a cooperative V2G system, a potential game is formulated to achieve the optimal social welfare of the V2G system. The existence and uniqueness of the Nash equilibrium of these two games are validated. Our simulation results show that the proposed game theoretic approaches can motivate EVs to smooth out the power fluctuations from the grid while EVs schedule their charging/discharging activities to maximize their utilities. This demonstrates the effectiveness of the use of the V2G game in providing regulation services to the grid. Through cooperation and extra information exchange, the social welfare of EVs and the EV aggregator can be improved to the global optimum and the V2G regulation services can also achieve near-optimal performance.

Toward Secure Data Sharing for the IoV: A Quality-Driven Incentive Mechanism With On-Chain and Off-Chain Guarantees

Currently, data sharing for the Internet of Vehicles (IoV) applications has drawn much attention in the framework of developing smart cities and smart transportation. A critical challenge for data sharing is to incentivize users to participate in collecting and sharing data. The traditional incentive mechanism of crowdsourcing is not practical for IoV because of its trust issues. Although blockchain technology has been introduced to address trust issues and security challenges, ensuring trust in off-chain data for the blockchain-based approaches is still an open issue. In this article, we propose a quality-driven auction-based incentive mechanism based on a consortium blockchain that guarantees trust in both on-chain data and off-chain data. We first introduce a consortium blockchain that is used as an open and distributed hyperledger to address the security issue of on-chain data. Then, we formulate the problem as a reverse auction in which the platform acts as an auctioneer that purchases data from users. By utilizing a data quality-driven auction model, the evaluated data quality via expectation maximization is used to ensure the trust in off-chain data. The quality-driven, auction-based incentive mechanism can obtain the high-quality data and optimal social welfare with low social cost. Otherwise, we design a smart contract to perform the data sharing automatically. Finally, the extensive simulations show that our proposed algorithm achieves maximum social welfare, outperforms other solutions, and scales well when the number of users or tasks increase. Moreover, the performance of the smart contract shows its low computing cost.

Matching Supply and Demand with Mismatch-Sensitive Players

We study matching over time with short- and long-lived players who are very sensitive to mismatch. To characterize the mismatch, we model players' preferences as uniformly distributed on a circle, so the mismatch between two players is characterized by the one-dimensional circular angle between them. This framework allows us to capture matching processes in applications ranging from ride sharing to job hunting. Our analytical framework relies on threshold matching policies. If the matching process is controlled by a central planner (e.g. an online matching platform), the matching threshold reflects the trade-off between matching rate and matching quality. We further compare the centralized system with decentralized systems, where players choose their matching partners. We find that matching controlled by either side of the market may achieve optimal or near optimal social welfare, but have great impact on welfare allocation. In particular, letting long-lived players choose their matching partner leaves short-lived players with zero surplus. Moreover, we extend our model with player heterogeneity. Letting long-lived players choose their matching partner leads to better social welfare when the market of short-lived players is thick and the level of heterogeneity is significant. Otherwise, letting short-lived players choose matching partners is better.

Connections between mean-field game and social welfare optimization

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the ϵ-Nash equilibrium of the mean-field game coincides with the optimal solution to a modified social welfare optimization problem. This enables us to study the mean-field equilibrium using standard optimization theory. Based on this connection, we derive new results on the existence and uniqueness of the mean-field equilibrium. We also show that the mean-field equilibrium can be computed by a decentralized primal–dual algorithm. Numerical results are presented to validate the solution, and examples are provided to show the applicability of the proposed approach.

Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game

Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in a numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes sum of all players' payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is called a quantum social welfare advice (SWA). We show that any two-qubit pure entangled state, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task.

Auction Mechanisms in Cloud/Fog Computing Resource Allocation for Public Blockchain Networks

As an emerging decentralized secure data management platform, blockchain has gained much popularity recently. To maintain a canonical state of blockchain data record, proof-of-work based consensus protocols provide the nodes, referred to as miners, in the network with incentives for confirming new block of transactions through a process of "block mining" by solving a cryptographic puzzle. Under the circumstance of limited local computing resources, e.g., mobile devices, it is natural for rational miners, i.e., consensus nodes, to offload computational tasks for proof of work to the cloud/fog computing servers. Therefore, we focus on the trading between the cloud/fog computing service provider and miners, and propose an auction-based market model for efficient computing resource allocation. In particular, we consider a proof-of-work based blockchain network. Due to the competition among miners in the blockchain network, the allocative externalities are particularly taken into account when designing the auction mechanisms. Specifically, we consider two bidding schemes: the constant-demand scheme where each miner bids for a fixed quantity of resources, and the multi-demand scheme where the miners can submit their preferable demands and bids. For the constant-demand bidding scheme, we propose an auction mechanism that achieves optimal social welfare. In the multi-demand bidding scheme, the social welfare maximization problem is NP-hard. Therefore, we design an approximate algorithm which guarantees the truthfulness, individual rationality and computational efficiency. Through extensive simulations, we show that our proposed auction mechanisms with the two bidding schemes can efficiently maximize the social welfare of the blockchain network and provide effective strategies for the cloud/fog computing service provider.

On Designing Distributed Auction Mechanisms for Wireless Spectrum Allocation

Auctions are believed to be effective methods to solve the problem of wireless spectrum allocation. Existing spectrum auction mechanisms are all centralized and suffer from several critical drawbacks of the centralized systems, which motivates the design of distributed spectrum auction mechanisms. However, extending a centralized spectrum auction to a distributed one broadens the strategy space of agents from one dimension (bid) to three dimensions (bid, communication, and computation), and thus cannot be solved by traditional approaches from mechanism design. In this paper, we propose two distributed spectrum auction mechanisms, namely distributed VCG and FAITH. Distributed VCG implements the celebrated Vickrey-Clarke-Groves mechanism in a distributed fashion to achieve optimal social welfare, at the cost of exponential communication overhead. In contrast, FAITH achieves sub-optimal social welfare with tractable computation and communication overhead. We prove that both of the two proposed mechanisms achieve faithfulness, i.e., the agents’ individual utilities are maximized, if they follow the intended strategies. Besides, we extend FAITH to adapt to dynamic scenarios where agents can arrive or depart at any time, without violating the property of faithfulness. We implement distributed VCG and FAITH, and evaluate their performance in various setups. Evaluation results show that distributed VCG results in optimal allocation, while FAITH is more efficient in computation and communication.

Noncooperative Social Welfare Optimization With Resiliency Against Network Anomaly

This article presents a noncooperative game-theoretic framework to model the social welfare optimization (SWO) problem with load aggregators participating in integrated economic dispatch and demand response. In the proposed framework, distribution system operators interact with generation units and load aggregators to maximize the overall social welfare. The proposed SWO problem addresses practical system constraints and falls into the scope of mixed integer nonlinear programs, which cannot be well handled by existing distributed algorithms. The proposed SWO problem is formulated by a special noncooperative strategic game, known as the potential game, and solved by a revised version of the spatial adaptive play under network anomaly. It is shown that the proposed framework has guaranteed convergence to a Nash equilibrium that is also a global optimizer. Simulations on a 15-generator benchmark distribution network have been conducted to validate the proposed framework.

Secure and Efficient Vehicle-to-Grid Energy Trading in Cyber Physical Systems: Integration of Blockchain and Edge Computing

Smart grid has emerged as a successful application of cyber-physical systems in the energy sector. Among numerous key technologies of the smart grid, vehicle-to-grid (V2G) provides a promising solution to reduce the level of demand-supply mismatch by leveraging the bidirectional energy-trading capabilities of electric vehicles. In this paper, we propose a secure and efficient V2G energy trading framework by exploring blockchain, contract theory, and edge computing. First, we develop a consortium blockchain-based secure energy trading mechanism for V2G. Then, we consider the information asymmetry scenario, and propose an efficient incentive mechanism based on contract theory. The social welfare optimization problem falls into the category of difference of convex programming and is solved by using the iterative convex-concave procedure algorithm. Next, edge computing has been incorporated to improve the successful probability of block creation. The computational resource allocation problem is modeled as a two-stage: 1) Stackelberg leader-follower game and 2) the optimal strategies are obtained by using the backward induction approach. Finally, the performance of the proposed framework is validated via numerical results and theoretical analysis.

QoI-aware incentive for multimedia crowdsensing enabled learning system

While much research has been devoted to algorithm improvement of the machine learning model for multimedia applications, relatively little research has focused on the acquisition of massive multimedia datasets with strict data demands for model training. In this paper, we propose a Quality-of-Information (QoI) aware incentive mechanism in multimedia crowdsensing, with the objective of promoting the growth of an initial training model. We begin with a reverse auction incentive model to maximize social welfare while meeting the requirements in quality, timeliness, correlation, and coverage. Then, we discuss how to achieve the optimal social welfare in the presence of an NP-hard winner determination problem. Lastly, we design an effective incentive mechanism to solve the auction problem, which is shown to be truthful, individually rational and computationally efficient. Our evaluation study is carried out using a real multimedia dataset. Extensive simulation results demonstrate that the proposed incentive mechanism produces close-to-optimal social welfare noticeably, while accompanied by accelerating the growth of the machine learning model with a high-QoI dataset.

Comparisons of Exhaustive and Nonexhaustive M/M/1/N Queues with Working Vacation and Threshold Policy

This paper compares the performance of exhaustive and nonexhaustive M/M/1/N queues with working vacation and threshold policy. In an exhaustive queue, the server slows down its service rate only when no customers exist in the system, and turns to normal service until the number of customers achieves a threshold. However, in a nonexhaustive queue, the server switches service rate between a low and a high value depending on system congestion. To get equilibrium arrival rate of customers and social welfare for the two types of queues, we first derive queue length distributions and expected busy circle. Then, by making sensitivity analysis of busy circle, system cost, arrival rate and optimal social welfare, we find that customers tend to join exhaustive queues instead of nonexhaustive queues, and the optimal threshold in an exhaustive queue is probably inconsistent with the one in a nonexhaustive queue. Moreover, in general, whether to consider system cost or not in social welfare will obviously affect the tendencies of optimal arrival rate and optimal social welfare with the threshold and system capacity for the two types of queues, especially for the nonexhaustive queues, and then affect the final decisions of social planner or system manager.