Nash and Wardrop Equilibria in Aggregative Games With Coupling Constraints

We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash and Wardrop equilibria. By exploiting a characterization of th...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 64; no. 4; pp. 1373 - 1388
Main Authors Paccagnan, Dario, Gentile, Basilio, Parise, Francesca, Kamgarpour, Maryam, Lygeros, John
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Aggregates
Aggregative games
Algorithms
Cost function
Coupling
coupling constraints
Couplings
distributed algorithms
Economic models
Electric vehicles
Equilibrium
Game theory
Games
generalized Nash equilibrium
large-scale systems
Nash equilibrium
Route selection
Sociology
Statistics
vehicle routing
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Summary:We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash and Wardrop equilibria. By exploiting a characterization of the two equilibria as solutions of variational inequalities, we bound their distance with a decreasing function of the population size. As second contribution, we propose two decentralized algorithms that converge to such equilibria and are capable of coping with constraints coupling the strategies of different agents. Finally, we study the applications of charging of electric vehicles and of route choice on a road network.
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2849946