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dc.contributor.author
Gentile, Basilio
dc.contributor.supervisor
Lygeros, John
dc.contributor.supervisor
Zampieri, Sandro
dc.contributor.supervisor
Hespanha, João
dc.date.accessioned
2018-09-13T05:47:39Z
dc.date.available
2018-09-12T14:37:44Z
dc.date.available
2018-09-13T05:47:39Z
dc.date.issued
2018
dc.identifier.uri
http://hdl.handle.net/20.500.11850/289079
dc.identifier.doi
10.3929/ethz-b-000289079
dc.description.abstract
This thesis studies equilibrium problems in aggregative games. A game describes the interaction among selfish rational agents, each of them choosing his strategy to optimize his own cost function, which depends also on the strategies of the other agents. In particular, the thesis focuses on aggregative games, where the cost of each agent is a sole function of his strategy and of the average agents’ strategy. Not only such class of games can model a wide spectrum of applications, ranging from traffic or transmission networks to electricity or commodity markets, but it also lends itself to an elegant mathematical analysis. The first part of the thesis investigates the relation between Nash and Wardrop equilibria, which are two classical concepts in game theory. Thanks to the powerful framework of variational inequalities, we derive bounds on the distance between the two equilibria and use them to show that the agents’ strategies at the Nash equilibrium converge to those at the Wardrop equilibrium, when the number of agents grows to infinity. Moreover, we propose novel sufficient conditions to guarantee uniqueness of the Nash equilibrium for a specific aggregative game, which is often used in applications. The second part of the thesis is dedicated to the design of algorithms that converge to Nash equilibrium and to Wardrop equilibrium in presence of constraints coupling the agents’ strategies. Due to privacy issues and to the large number of agents at hand in real-life applications, centralized solutions might not be desirable. Hence, we first propose two parallel algorithms, where a central operator gathers and broadcasts aggregate information to coordinate the computations carried out by the agents. Then we design a distributed algorithm that only relies on local communications among the agents. We test the proposed algorithms in three case studies, where we also numerically verify the results of the first part of the thesis. The last part of the thesis introduces the novel concept of equilibrium with inertia. Both classical Nash and Wardrop equilibria assume that each agent has the flexibility to change his strategy whenever this leads to an improvement. In some applications, however, this hypothesis is not realistic. We show that introducing an inertial coefficient which penalizes action switches leads to a richer set of equilibria, which is however in general not convex. Since classical algorithms for Nash and Wardrop equilibria cannot be used in presence of the inertial coefficients, we propose natural agents dynamics and guarantee their convergence to an equilibrium with inertial coefficients.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Game Theory
en_US
dc.subject
Algorithms
en_US
dc.subject
Aggregative Games
en_US
dc.subject
Networks
en_US
dc.title
Equilibria in aggregative games
en_US
dc.type
Doctoral Thesis
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2018-09-13
ethz.size
148 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
ethz.identifier.diss
24975
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02650 - Institut für Automatik / Automatic Control Laboratory
en_US
ethz.date.deposited
2018-09-12T14:37:44Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2018-09-13T05:47:47Z
ethz.rosetta.lastUpdated
2021-02-15T01:44:22Z
ethz.rosetta.versionExported
true
ethz.COinS
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