On the Efficiency of Nash Equilibria in Aggregative Charging Games

Paccagnan, Dario; Parise, Francesca; Lygeros, John

doi:10.1109/lcsys.2018.2845674

Cited by 6 publications

(6 citation statements)

References 28 publications

(85 reference statements)

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“…Applications in smart grid, transportation, and IT are envisioned among the possible beneficiaries [5], [6], [7], [8], [9]. In connection with public infrastructures, a large number of studies followed the seminal work of Wardrop [10], focusing on the relation between the achieved equilibria and the social welfare; among recent results, we mention [11], [12], [7], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach

Fele

Margellos

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Motivated by electric vehicle charging control problems, we consider multi-agent noncooperative games where, following a data driven paradigm, unmodeled externalities acting on the players' objective functions are represented by means of scenarios. Building upon recent developments in scenario-based optimization, based on the evaluation of the computed solution, we accompany the Nash equilibria of the uncertain game with an a posteriori probabilistic robustness certificate, providing confidence on the probability that the computed solution remains unaffected when a new uncertainty realisation is encountered. The latter constitutes, to the best of our knowledge, the first application of the so-called scenario approach to multi-agent Nash equilibrium problems. The efficacy of our approach is demonstrated in simulation for the charging coordination of an electric vehicle fleet.

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Section: Introductionmentioning

confidence: 99%

Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach

Fele

Margellos

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…, we have c1γ 2 0 /η0 + c2γ0/η0 < c3, implying that det(α k I − Ĥk ) > 0. Thus for all k ≥ 1, we have ρ( Ĥk ) < α k = 1 − 0.5γ k η k µg provided that γ0 satisfies (16). We can conclude that for all k ≥ 1, we have…”

Section: Lemmamentioning

confidence: 85%

“…The charging management of electric vehicles (EV) in an electricity market is an instance of aggregative games [4], [6], [16]. The energy price at every time instant relies on the total energy demand of all EVs.…”

Section: Numerical Studiesmentioning

confidence: 99%

“…Within this avenue, [15] studies a noncooperative spectrum sharing game with two players and provides the upper bound of PoA at a high signal to noise ratio. [16] considers aggregative charging games in smart grids, and provides the upper bounds of PoA for three types of charging price functions. In addition to considering the efficiency under the worst Nash equilibrium, how to obtain a best Nash equilibrium that optimizes the social welfware/cost is also very meaningful, and is referred as the optimal NE problem [17].…”

Section: Introductionmentioning

confidence: 99%

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Distributed coordination for seeking the optimal Nash equilibrium of aggregative games

Ma¹,

Lei²,

Peng³

et al. 2022

Preprint

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This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has no incentive to deviate from the equilibrium under its private objective. Meanwhile, the agents can coordinate to optimize the social cost within the set of Nash equilibria of the underlying game. Such an optimal Nash equilibrium problem can be modeled as a distributed optimization problem with variational inequality constraints. We consider the scenario where the objective functions of both the underlying game and social cost optimization problem have a special aggregation structure. Since each player only has access to its local objectives while cannot know all players' decisions, a distributed algorithm is highly desirable. By utilizing the Tikhonov regularization and dynamical averaging tracking technique, we propose a distributed coordination algorithm by introducing an incentive term in addition to the gradient-based Nash equilibrium seeking, so as to intervene players' decisions to improve the system efficiency. We prove its convergence to the optimal Nash equilibrium of a monotone aggregative game with simulation studies.

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“…All the proofs are reported in the Appendix (Section 5.3). The results presented in this chapter have been published in [Pac+18;PPL18]. Specifically, we consider a sequence of games (G M ) ∞ M =1 .…”

Section: Equilibria and Efficiency In Large Populationsmentioning

confidence: 99%

Distributed Control and Game Design: From Strategic Agents to Programmable Machines

Paccagnan¹

2018

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i sincere thanks goes to you for your support and collaboration during the early stages of my PhD. I remember vividly how much help and enthusiasm you put in teaching me how to write my "first article". If all of this is possible, it is in good part also thanks to you.The atmosphere we breath at IfA is absolutely incredible: a great mix of hardworking, positive energy, and friendship. Sometimes, bent over our papers, we seem to forget how lucky we are. Fortunately (or not), as soon as we step out of the ETH domain, we get reminded of what a privilege this is. I would like to express my greatest gratitude to all those people that made this place what it is. In this regard, there are many colleagues I should thank, but I limit myself to the essential. First of all, I would like to thank Basilio and Francesca for sharing with me a good half of their PhDs, and countless hours on the board conjecturing results that would be proved wrong only a few hours later. I wish both of you a brilliant career as you truly deserve. A very special thanks is due to Nicolò for sharing innumerable moments inside and outside of the office, for the many jokes we have been laughing of, and for the unmissable extra slice of cake (Lucia's). A big thanks goes to the Italian Gang -Basilio, Francesca, Nicolò, Giampaolo, Marcello, Saverio -for the countless adventures, and for making me feel as IfA was the extension of my time in high school. Thank you Tony for being such a positive, cheerful and selfless person. Thank you Peyman for the numerous research discussions we had: I feel there is a lot to learn form you. Thanks to the dream team -Juan, Marcello, Paul -for all the mountains adventures we shared: I will hardly forget when we set foot on the Dammazwillinge for the first time. I am confident you will not forget either. A special thanks goes to Paul for being a terrific office mate, and for sharing the first years of your PhD with me, often out in the Alps. At this point, I feel I owe a big thanks to our secretaries, Sabrina and Tanja, for making everything run incredibly smooth and for being extremely helpful with really anything. "If there is a solution, we will find it" Sabrina told me once, and this pretty much says it all.At a personal level, I would like to thank all my friends in Zurich and elsewhere, in particular Chiara for the gazillions hours we spent climbing together, Federica for being a terrific housemate, Martina and Alessandro for hosting me after my return from the US. A line of his own is needed (and probably not enough) to thank Alessio: a very special thought goes to you for all the things we went through together, way too many to recall. I will never forget the 20-hours day on the Allighesi ferrata, our first climbing route in the dolomites, or simply the usual giro di Ca' Tron. Amongst everything, I would like to thank you for teaching me to be ambitious, to fight, to never give up and to endure pain. Last, I want to thank you for always finding time to meet with me (the usual run) when I come back from Zurich, reg...

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On the Efficiency of Nash Equilibria in Aggregative Charging Games

Cited by 6 publications

References 28 publications

Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach

Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach

Distributed coordination for seeking the optimal Nash equilibrium of aggregative games

Distributed Control and Game Design: From Strategic Agents to Programmable Machines

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