Generalized Nash Equilibrium Model of the Service Provisioning Problem in Multi-Cloud Competitions

We propose a new solution concept for generalized Nash equilibrium problems. This concept leads, under suitable assumptions, to unique solutions, which are generalized Nash equilibria and the result of a mathematical procedure modeling the process of finding a compromise. We first compute the favorite strategy for each player, if he could dictate the game, and use the best response on the others’ favorite strategies as starting point. Then, we perform a tracing procedure, where we solve parametrized generalized Nash equilibrium problems, in which the players reduce the weight on the best possible and increase the weight on the current strategies of the others. Finally, we define the limiting points of this tracing procedure as solutions. Under our assumptions, the new concept selects one reasonable out of typically infinitely many generalized Nash equilibria.

This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector that minimizes the cost for each player. Unlike most of the existing algorithms for GNEP, which require full information exchange among all players, this paper considers a more realistic scenario where players can only communicate with a subset of players through a connectivity graph. The proposed algorithm enables each player to estimate the decisions of other players and update their own and others’ estimates through local communication with their neighbors. By introducing a network Lagrangian function and applying the Douglas-Rachford splitting method (DR), the GNEP is reformulated as a zero-finding problem. It is shown that the DR method can find the generalized Nash equilibrium (GNE) of the original problem under some mild conditions.

Two-stage game theoretical framework for IaaS market share dynamics

Fog computing is a paradigm which brings computing, storage, and networking closer to end users and devices for better service provisioning. One of the crucial factors towards the success of fog computing is how to incentivize the individual users' edge resources, thereby opening the era of user- participated fog computing. In this paper, we provide an economic analysis of such user-oriented fog computing by modeling a market consisting of ISP (Infrastructure and Service Provider), SUs (end Service Users), and EROs (Edge Resource Owners) as a noncooperative game. In this market, ISP, which provides a platform of fog computing, behaves as a mediator or a broker to lease the edge resources from EROs and provide various services to SUs. In our game formulation, a two-stage dynamic game is used, where in each stage there exists another dynamic game, one for between ISP and EROs and another for between ISP and SUs, to model the market more practically. Despite this complex game structure, we provide a closed- form equilibrium analysis, which gives an insight of how much economic benefits are obtained by ISP, SUs, and EROs under what conditions.

Generalized Nash equilibrium problems (GNEPs) allow, in contrast to standard Nash equilibrium problems, a dependence of the strategy space of one player from the decisions of the other players. In this paper, we consider jointly convex GNEPs which form an important subclass of the general GNEPs. Based on a regularized Nikaido-Isoda function, we present two (nonsmooth) reformulations of this class of GNEPs, one reformulation being a constrained optimization problem and the other one being an unconstrained optimization problem. While most approaches in the literature compute only a so-called normalized Nash equilibrium, which is a subset of all solutions, our two approaches have the property that their minima characterize the set of all solutions of a GNEP. We also investigate the smoothness properties of our two optimization problems and show that both problems are continuous under a Slater-type condition and, in fact, piecewise continuously differentiable under the constant rank constraint qualification. Finally, we present some numerical results based on our unconstrained optimization reformulation.

Mobile Network Operators (MNO) can reduce their Capital and Operational Expenditure (CAPEX) and (OPEX) with the help of tower sharing approach by utilizing the physical infrastructure equipped by a third party tower provider to expand their network coverage. Moreover, Computing Resource Providers (CRP) are also setting up their micro-datacenters at tower stations to provide the Multi-access Edge Computing (MEC) services by cooperating with tower providers. Since both the communication and computing services contribute to the task offloading in MEC, the resource allocation has become a challenging problem. In this paper, we formulate the joint uplink, downlink, and computing resources allocation problem in which the objectives of both MNOs and CRP are to minimize their OPEX. The task offloading is modeled as a network of queues where the end-to-end latency is calculated based on the performance of the queue network. Then, the formulated problem is transformed into a Generalized Nash Equilibrium Problem (GNEP) to capture the conflicting interests in the resource allocation among MNOs and CRP. To solve the formulated GNEP efficiently, two decentralized algorithms are proposed by introducing the penalty parameters to the coupling constraints. In addition, the convergence and performance of the algorithms on different parameters are analyzed.

Cloud computing has taken the IT and business world by storm through its cost savings and quick-and-easy adoption. Currently, fixed price model is dominating the pricing schemes in the cloud market. However, this model is unable to reflect the current market needs for cost savings as the number of cloud provider and user increases. As a result, a dynamic pricing scheme has emerged as an attractive strategy to better cope with the unpredictable cloud demand. This paper proposed a dynamic pricing scheme that provides fairness among the service providers in a multi-cloud environment. The scheme adjusts the price accordingly to encourage the low utilized resources’ usage and discourage over utilized resources’ usage. The evaluation results showed that the proposed scheme is able to reduce the cost of the end user when running compute-intensive and data-intensive jobs in the multi-cloud environment.

Understanding health information can be difficult, which can limit people's ability to manage their health and adopt healthy practices, leading to poorer health outcomes. This study aimed to evaluate a verbal health literacy training initiative designed to support clear conversations between health service providers and users. The initiative incorporated Teach-back, Chunk and Check, Simple Language, and Open Questions, alongside implementation support from a health literacy officer. A concurrent mixed-methods evaluation was conducted across two health programmes serving a population of approximately one million people in the United Kingdom: A Pulmonary Rehabilitation Programme delivered by five physiotherapists in a hospital setting, and a Weight Management Programme delivered by 12 health improvement advisors within a regional government authority. The evaluation comprised five components: (1) Surveys of 110 service providers' perceptions of the training; (2) Observations of 11 service providers before and after training; (3) Two focus groups with 11 service providers six months post-training; (4) Change in 73 service users' health literacy levels using two domains of the Health Literacy Questionnaire; (5) Change in service users' health and wellbeing between baseline and programme completion. Service providers found the initiative useful. Changes in communication practice, such as increased use of Chunk and Check and Open Questions, were observed. Both programmes were delivered in group settings. Teach-back was reported to be challenging to apply in this context but beneficial in one-to-one interactions in wider practice. Implementation support from the health literacy officer was helpful but difficult to deliver to busy teams. Service users' health literacy levels improved by the end of their programme, but there was no evidence that the initiative improved health and wellbeing outcomes. For example, no significant difference was observed in the primary outcome for Weight Management participants in the intervention group compared with controls (0.2kg, - 2.3 to 1.9; p = 0.84). In this small evaluation, the initiative was well received and enhanced service providers' communication skills. Further evaluation of a strengthened initiative should focus on controlled before-and-after designs using larger samples to determine the effect on service users' health literacy and health and wellbeing outcomes.

The HUSK projects, involving collaboration between service users, providers, educators, and researchers, coincided with the reorganization of national government services (NAV). The NAV reorganization brought together employment services, social insurance, and municipal social service benefits, and called for a service model where users would be empowered to influence the provision of services. In this analysis of the HUSK cases the authors focus on the relationship between the service user and the service provider, identifying themes in two broad domains: concepts of the individual that included the service user and the service provider and concepts of the relationship that included power, role, activity, interaction, and communication. Within each theme, the analysis highlights the transition from a traditional or historical state to a new or desired state and draws upon some of the classic literature that frames the encounters between service users and providers.

The generalized Nash equilibrium problem is an extension of the standard Nash equilibrium problem where both the utility function and the strategy space of each player depend on the strategies chosen by all other players. Recently, the generalized Nash equilibrium problem has emerged as an effective and powerful tool for modeling a wide class of problems arising in many fields and yet solution algorithms are extremely scarce. In this paper, using a regularized Nikaido-Isoda function, we reformulate the generalized Nash equilibrium problem as a mathematical program with complementarity constraints (MPCC). We then propose a suitable method for this MPCC and under some conditions, we establish the convergence of the proposed method by showing that any accumulation point of the generated sequence is a M-stationary point of the MPCC. Numerical results on some generalized Nash equilibrium problems are reported to illustrate the behavior of our approach.

We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few results are known in the literature. We present a new approach to characterize equilibria via a convexification technique using the Nikaido–Isoda function. To any given instance of the GNEP, we construct a set of convexified instances and show that a feasible strategy profile is an equilibrium for the original instance if and only if it is an equilibrium for any convexified instance and the convexified cost functions coincide with the initial ones. We develop this convexification approach along three dimensions: We first show that for quasi-linear models, where a convexified instance exists in which for fixed strategies of the opponent players, the cost function of every player is linear and the respective strategy space is polyhedral, the convexification reduces the GNEP to a standard (non-linear) optimization problem. Secondly, we derive two complete characterizations of those GNEPs for which the convexification leads to a jointly constrained or a jointly convex GNEP, respectively. These characterizations require new concepts related to the interplay of the convex hull operator applied to restricted subsets of feasible strategies and may be interesting on their own. Note that this characterization is also computationally relevant as jointly convex GNEPs have been extensively studied in the literature. Finally, we demonstrate the applicability of our results by presenting a numerical study regarding the computation of equilibria for three classes of GNEPs related to integral network flows and discrete market equilibria.

BackgroundAn integrated chronic disease management (ICDM) model was introduced by the National Department of Health in South Africa to tackle the dual burden of HIV/AIDS and non-communicable diseases. One of the aims of the ICDM model is to reduce HIV-related stigma. This paper describes the viewpoints of service users and providers on HIV stigma in an ICDM model in rural South Africa.Materials and methodsA content analysis of HIV stigmatisation in seven primary health care (PHC) facilities and their catchment communities was conducted in 2013 in the rural Agincourt sub-district, South Africa. Eight Focus Group Discussions were used to obtain data from 61 purposively selected participants who were 18 years and above. Seven In-Depth Interviews were conducted with the nurses-in-charge of the facilities. The transcripts were inductively analysed using MAXQDA 2018 qualitative software.ResultsThe emerging themes were HIV stigma, HIV testing and reproductive health-related concerns. Both service providers and users perceived implementation of the ICDM model may have led to reduced HIV stigma in the facilities. On the other hand, service users and providers thought HIV stigma increased in the communities because community members thought that home-based carers visited the homes of People living with HIV. Service users thought that routine HIV testing, intended for pregnant women, was linked with unwanted pregnancies among adolescents who wanted to use contraceptives but refused to take an HIV test as a precondition for receiving contraceptives.ConclusionsAlthough the ICDM model was perceived to have contributed to reducing HIV stigma in the health facilities, it was linked with stigma in the communities. This has implications for practice in the community component of the ICDM model in the study setting and elsewhere in South Africa.

This paper studies the market interactions between MicroGrids (MGs) and Aggregators (AGs) from a noncooperative perspective. Specifically, we study a Generalized Nash Equilibrium Problem (GNEP), where players are the MGs and AGs, and aim at maximizing their respective benefits. MGs' actions are the generated energy as well as the traded energy with other MGs, whereas AGs actions are the load scheduling of their subscribed users. The variational solutions of the GNEP are characterized and a distributed algorithm for its computation is proposed. By numerical simulations, it is shown that the variational solutions of the GNEP perform close to the solution of the network utility maximization problem.

BackgroundChildren and families seeking asylum have significant unmet health needs. The Respond service was established in response to high numbers of families seeking asylum arriving in Camden (London, UK) in August 2021 and delivers hospital and community-based holistic assessment and infectious disease screening for this population. Families are seen in a joint appointment by a multidisciplinary team of adult and paediatric health professionals. We explored the priorities, barriers and experiences around healthcare access among families using the service and the acceptability and perceived effectiveness of a family-centred approach from the perspective of service users, service providers and key stakeholders.MethodsWe employed qualitative and quantitative approaches. Questionnaires and semistructured interviews were completed between July and September 2022. Questionnaires were built on Google Forms and Envoy Messenger (Healthcare Communications). Thematic analysis was performed and structured by key themes. Data were analysed with the assistance of NVivo.ResultsAccess to dental care, primary care and immunisations were identified as key priorities for families. Significant barriers of access to care included understanding (language), situation (temporary accommodation) and awareness (unfamiliarity with systems, digital poverty, signposting). The Respond family-centred model was positively received by service users, service providers and stakeholders. Benefits included the provision of holistic family-centred care and support, efficiency and value-for-money for the health service. Areas needing ongoing input were language barriers, educational support for staff and service users and continued collaboration and co-creation between service providers and service users.ConclusionRecognising the priorities and barriers identified in this study is crucial for enhancing access to and utilisation of services within this underserved community. The Respond family-centred model was well received and perceived as effective by service users, providers and stakeholders. It serves as a foundational framework for developing tailored services for children and families seeking asylum across the UK and internationally.

Non-additive network pricing with non-cooperative mobility service providers