Decomposition algorithms for generalized potential games

Facchinei, Francisco; Piccialli, Veronica; Sciandrone, Marco

doi:10.1007/s10589-010-9331-9

Cited by 114 publications

(131 citation statements)

References 23 publications

(44 reference statements)

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“…Since (i) the payoff function Θ p of PaaS provider depends only on his own strategies N s , (ii) the payoff function Θ s of each SaaS provider s only depends on his own strategies X s and R P s , and (iii) constraints (17) and (18) are shared among the players, we can conclude that this game is a generalized potential game [27,34] where the potential function is simply the sum of the players payoff functions. This potential function represents a social welfare for the game.…”

Section: Potential Functionmentioning

confidence: 91%

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Generalized Nash equilibria for SaaS/PaaS Clouds

Anselmi

Ardagna

Passacantando

2014

European Journal of Operational Research

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Cloud computing is an emerging technology that allows to access computing resources on a pay-per-use basis. The main challenges in this area are the efficient performance management and the energy costs minimization.In this paper we model the service provisioning problem of Cloud Platform-as-aService systems as a Generalized Nash Equilibrium Problem and show that a potential function for the game exists. Moreover, we prove that the social optimum problem is convex and we derive some properties of social optima from the corresponding KarushKuhn-Tucker system. Next, we propose a distributed solution algorithm based on the best response dynamics and we prove its convergence to generalized Nash equilibria.Finally, we numerically evaluate equilibria in terms of their efficiency with respect to the social optimum of the Cloud by varying our algorithm initial solution. Numerical results show that our algorithm is scalable and very efficient and thus can be adopted for the run-time management of very large scale systems.

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Section: Potential Functionmentioning

confidence: 91%

“…If we denote L i k ≥ 0, for k ∈ A and i = 1, 2, 3, the KKT multipliers associated to constraints (25) and (26), and L 4 ≥ 0, the multiplier associated to constraint (27), then the KKT system is the following:…”

Section: Thus the Hessian Matrix Of H Ismentioning

confidence: 99%

Generalized Nash equilibria for SaaS/PaaS Clouds

Anselmi

Ardagna

Passacantando

2014

European Journal of Operational Research

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“…Since each agent has a pay-off function of the same structure, the resulting game is a potential game, Facchinei et al (2011);Voorneveld (2000).…”

Section: Electric Vehicle Charging Control Problemmentioning

confidence: 99%

On the connection between Nash equilibria and social optima in electric vehicle charging control games

2017

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Abstract:We consider the problem of optimal charging of heterogeneous plug-in electric vehicles (PEVs). We approach the problem as a multi-agent game in the presence of constraints and formulate an auxiliary minimization program whose solution is shown to be the unique Nash equilibrium of the PEV charging control game, for any finite number of possibly heterogeneous agents. Assuming that the parameters defining the constraints of each vehicle are drawn randomly from a given distribution, we show that, as the number of agents tends to infinity, the value of the game achieved by the Nash equilibrium and the social optimum of the cooperative counterpart of the problem under study coincide for almost any choice of the random heterogeneity parameters. To the best of our knowledge, this result quantifies for the first time the asymptotic behaviour of the price of anarchy for this class of games. A numerical investigation to support our result is also provided.

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“…Utility functions satisfying (6) can be found in so called "network transmission games," see, e.g., Facchinei et al (2011) and references therein, which are somewhat similar to Rosenthal's (1973) congestion games, but do not belong to the class. There is a directed graph with the set of links E; each player i ∈ N is assigned a path π i ⊆ E in the graph (between a source and a target) and sends a flow x i ∈ [0, b i ] ⊂ R along the path, getting a reward w i (x i ) depending on her flow and bearing costs e∈π i c e ( j: e∈π j x j ) depending on the total flow through each link…”

Section: Games With Structured Utilitiesmentioning

confidence: 99%