Nash Equilibria, Variational Inequalities, and Dynamical Systems

Cavazzuti, E.; Pappalardo, M.; Passacantando, Mauro

doi:10.1023/a:1016056327692

Cited by 82 publications

(53 citation statements)

References 5 publications

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“…formulated the Cournot Nash game as a differential variational inequality to solve a network oligopolistic competition problem in a supply chain. The quasi-variational inequality approach, developed by Cavazzuti et al (2002) and Pang (2002), dealt with joint constraints. Adida and Perakis (2006) and Adida and Perakis (2010) showed the existence and uniqueness of generalized Nash equilibrium based on Pang (2002) and then used robust optimization to address demand uncertainty.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic Pricing and Inventory Policies: A Strategic Analysis of Dual Channel Supply Chain Design

2010

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his paper presents a continuous time optimization model for a dynamic pricing and inventory control problem in a dual-channel supply chain system. We consider a manufacturer's redesign of traditional channel structures, based on customer behaviors, by engaging in direct Internet sales. While the manufacturer and its retailer set optimal pricing and inventory policies dynamically, this study considers both vertical integration and competition of two channels. For the former case, a continuous time optimal control problem is modeled, while for the latter a differential quasi-variational inequality (DQVI) formulation is applied to solve as a Cournot-Nash-Bertrand game. We provide implications for optimal strategies and note the effect of a customer acceptance index.

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Section: Literature Reviewmentioning

confidence: 99%

Dynamic Pricing and Inventory Policies: A Strategic Analysis of Dual Channel Supply Chain Design

2010

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“…Each IaaS, in turn, wants to maximize the revenues obtained providing the resources. To capture the behavior of SaaSs and IaaSs in this conflicting situation, in which the best choice for one depends on the choices of the others, we model such problem as a Generalized Nash Equilibrium Problem (GNEP), in which both the objective function and the feasible region of each player depend on the strategies chosen by the other players (see, e.g., [23], [27], [29], [56]). Then, we propose a distributed algorithm which converges to a Generalized Nash Equilibrium after a finite number of iterations.…”

Section: Introductionmentioning

confidence: 99%

Generalized Nash Equilibria for the Service Provisioning Problem in Multi-Cloud Systems

Ardagna

Ciavotta

Passacantando

2017

IEEE Trans. Serv. Comput.

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Abstract-The adoption of Cloud technologies is steadily increasing. In such systems, applications can benefit from nearly infinite virtual resources on a pay-per-use basis. However, being the Cloud massively multi-tenant and characterized by highly variable workloads the development of more and more effective provisioning policies assumes paramount importance. Boosted by the success of the Cloud, the application of Game Theory models and methodologies has also become popular, since they have been demonstrated to suit perfectly to Cloud social, economic, and strategic structures. This paper aims to study, model and efficiently solve the cost minimization problem associated with the service provisioning of SaaS virtual machines in multiple IaaSs. We propose a game-theoretic approach for the runtime management of resources from multiple IaaS providers to be allocated to multiple competing SaaSs, along with a cost model including revenues and penalties for requests execution failures. A distributed algorithm for identifying Generalized Nash Equilibria has been developed and analysed in detail. The effectiveness of our approach has been assessed by performing a wide set of analyses under multiple workload conditions. Results show that our algorithm is scalable and provides significant cost savings with respect to alternative methods (80% on average). Furthermore, increasing the number of IaaS providers SaaSs can achieve 9-15% cost savings from the workload distribution on multiple IaaSs.

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“…To capture the behavior of SaaSs and IaaSs in this conflicting situation, in which the best choice for one depends on the choices of the others, we recur to the Generalized Nash Equilibrium (GNE) concept (see e.g., (Bigi et al 2013, Cavazzuti et al 2002, Debreu 1952, Facchinei and Kanzow 2010a, Rosen 1965). GNE is an extension of the Nash equilibrium, in which not only the objective function but also the feasible region of each player depend on the strategies chosen by the other players.…”

Section: Introductionmentioning

confidence: 99%

Service Provisioning Problem in Cloud and Multi-Cloud Systems

Passacantando

Ardagna

Savi

2016

INFORMS Journal on Computing

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Cloud Computing is a new emerging paradigm that aims at streamlining the on-demand provisioning of resources as services, providing end-user with flexible and scalable services accessible through the Internet on a pay-per-use basis. Since modern Cloud systems operate in an open and dynamic world characterized by continuous changes, the development of efficient resource provisioning policies for Cloud-based services becomes increasingly challenging. This paper aims to study the hourly basis service provisioning problem through a generalized Nash game model. We take the perspective of SaaS (Software as a Service) providers which want to minimize the costs associated with the virtual machine instances allocated in a multi-IaaSs (Infrastructure as a Service) scenario, while avoiding incurring in penalties for requests execution failures and providing quality of service guarantees. SaaS providers compete and bid for the use of infrastructural resources, while the IaaSs want to maximize their revenues obtained providing virtualized resources.We propose a solution algorithm based on the best-reply dynamics, which is suitable for a distributed implementation. We demonstrate the effectiveness of our approach by performing numerical tests, considering multiple workloads and system configurations. Results show that our algorithm is scalable and provides significant cost savings with respect to alternative methods (5% on average but up to 260% for individual SaaS providers). Furthermore, varying the number of IaaS providers 8-15% cost savings can be achieved from the workload distribution on multiple IaaSs.

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Nash Equilibria, Variational Inequalities, and Dynamical Systems

Abstract: In this paper we introduce some relationships between Nash equilibria, variational equilibria and dynamical equilibria for noncooperative games.

Cited by 82 publications

References 5 publications

Dynamic Pricing and Inventory Policies: A Strategic Analysis of Dual Channel Supply Chain Design

Dynamic Pricing and Inventory Policies: A Strategic Analysis of Dual Channel Supply Chain Design

Generalized Nash Equilibria for the Service Provisioning Problem in Multi-Cloud Systems

Service Provisioning Problem in Cloud and Multi-Cloud Systems

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