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Journal ArticleDOI

Price of anarchy in electric vehicle charging control games: When Nash equilibria achieve social welfare

01 Oct 2018-Automatica (Pergamon)-Vol. 96, Iss: 96, pp 150-158
TL;DR: In this paper, the authors considered the problem of optimal charging of plug-in electric vehicles (PEVs) as a multi-agent game, where vehicles/agents are heterogeneous since they are subject to possibly different constraints.
About: This article is published in Automatica.The article was published on 2018-10-01 and is currently open access. It has received 34 citations till now. The article focuses on the topics: Price of anarchy & Nash equilibrium.
Citations
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Journal ArticleDOI
TL;DR: This work proposes simple semidecentralized integral dynamics and proves their global asymptotic convergence to a variational generalized aggregative or Nash equilibrium based on Lyapunov arguments and invariance techniques for differential inclusions.
Abstract: We consider continuous-time equilibrium seeking in a class of aggregative games with strongly convex cost functions and affine coupling constraints. We propose simple semidecentralized integral dynamics and prove their global asymptotic convergence to a variational generalized aggregative or Nash equilibrium. The proof is based on Lyapunov arguments and invariance techniques for differential inclusions.

61 citations

Journal Article
TL;DR: In a system where noncooperative agents share a common resource, the price of anarchy is proposed, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system.
Abstract: In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.

46 citations

Journal ArticleDOI
TL;DR: A new methodological approach is proposed to establish full characterizations of an optimal scheduling policy that enable the development of scalable computational approaches and achieves close-to-optimal performance in numerical experiments with real-world electricity pricing and solar generation data.

20 citations

Posted Content
28 Mar 2018
TL;DR: This work addresses the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints and designs a single-layer, fixed-step algorithm with convergence guarantee for general (non cocoercive, non-strictly) monotone aggregation games.
Abstract: We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

18 citations

Journal ArticleDOI
TL;DR: This work considers a multi-agent noncooperative game with agents' objective functions being affected by uncertainty, and accompanies the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected when a new uncertainty realization is encountered.
Abstract: We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set - a key concept in scenario-based optimization - can be directly obtained as a byproduct of the proposed solution methodology. Finally, we illustrate how to overcome differentiability issues, arising due to the introduction of scenarios, and compute a Nash equilibrium solution in a decentralized manner. We demonstrate the efficacy of the proposed approach on an electric vehicle charging control problem.

16 citations

References
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Book
01 Jan 1989
TL;DR: This work discusses parallel and distributed architectures, complexity measures, and communication and synchronization issues, and it presents both Jacobi and Gauss-Seidel iterations, which serve as algorithms of reference for many of the computational approaches addressed later.
Abstract: gineering, computer science, operations research, and applied mathematics. It is essentially a self-contained work, with the development of the material occurring in the main body of the text and excellent appendices on linear algebra and analysis, graph theory, duality theory, and probability theory and Markov chains supporting it. The introduction discusses parallel and distributed architectures, complexity measures, and communication and synchronization issues, and it presents both Jacobi and Gauss-Seidel iterations, which serve as algorithms of reference for many of the computational approaches addressed later. After the introduction, the text is organized in two parts: synchronous algorithms and asynchronous algorithms. The discussion of synchronous algorithms comprises four chapters, with Chapter 2 presenting both direct methods (converging to the exact solution within a finite number of steps) and iterative methods for linear

5,597 citations

Book ChapterDOI
TL;DR: In this article, a simplification of the structure of the proofs has been made possible through use of the concept of an abstract economy, a generalization of that of a game, and proofs of the existence of an equilibrium are given for an integrated model of production, exchange and consumption.
Abstract: A. Wald has presented a model of production and a model of exchange and proofs of the existence of an equilibrium for each of them. Here proofs of the existence of an equilibrium are given for an integrated model of production, exchange and consumption. In addition the assumptions made on the technologies of producers and the tastes of consumers are significantly weaker than Wald's. Finally a simplification of the structure of the proofs has been made possible through use of the concept of an abstract economy, a generalization of that of a game. Introduction L. Walras [ 24 ] first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers, and the equilibrium condition that supply equal demand on every market. It was assumed that each consumer acts so as to maximize his utility, each producer acts so as to maximize his profit, and perfect competition prevails, in the sense that each producer and consumer regards the prices paid and received as independent of his own choices. Walras did not, however, give any conclusive arguments to show that the equations, as given, have a solution.

4,229 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present three examples of the mean-field approach to modelling in economics and finance (or other related subjects) and show that these nonlinear problems are essentially well-posed problems with unique solutions.
Abstract: We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects...). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited information (or visibility) on the “game”. Each player chooses his optimal strategy in view of the global (or macroscopic) informations that are available to him and that result from the actions of all players. In the three examples we mention here, we derive a mean-field problem which consists in nonlinear differential equations. These equations are of a new type and our main goal here is to study them and establish their links with various fields of Analysis. We show in particular that these nonlinear problems are essentially well-posed problems i.e., have unique solutions. In addition, we give various limiting cases, examples and possible extensions. And we mention many open problems.

2,385 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system.

1,346 citations

Journal ArticleDOI
01 Jan 2011
TL;DR: Conceptual frameworks for actively involving highly distributed loads in power system control actions and some of the challenges to achieving a load control scheme that balances device- level objectives with power system-level objectives are discussed.
Abstract: This paper discusses conceptual frameworks for actively involving highly distributed loads in power system control actions. The context for load control is established by providing an overview of system control objectives, including economic dispatch, automatic generation control, and spinning reserve. The paper then reviews existing initiatives that seek to develop load control programs for the provision of power system services. We then discuss some of the challenges to achieving a load control scheme that balances device-level objectives with power system-level objectives. One of the central premises of the paper is that, in order to achieve full responsiveness, direct load control (as opposed to price response) is required to enable fast time scale, predictable control opportunities, especially for the provision of ancillary services such as regulation and contingency reserves. Centralized, hierarchical, and distributed control architectures are discussed along with benefits and disadvantages, especially in relation to integration with the legacy power system control architecture. Implications for the supporting communications infrastructure are also considered. Fully responsive load control is illustrated in the context of thermostatically controlled loads and plug-in electric vehicles.

1,105 citations