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Nonatomic aggregative games with infinitely many types
- Source :
- European Journal of Operational Research. 301:1149-1165
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- We define and analyze the notion of variational Wardrop equilibrium for nonatomic aggregative games with an infinity of players types. These equilibria are characterized through an infinite-dimensional variational inequality. We show, under monotonicity conditions, a convergence theorem enables to approximate such an equilibrium with arbitrary precision. To this end, we introduce a sequence of nonatomic games with a finite number of players types, which approximates the initial game. We show the existence of a symmetric Wardrop equilibrium in each of these games. We prove that those symmetric equilibria converge to an equilibrium of the infinite game, and that they can be computed as solutions of finite-dimensional variational inequalities. The model is illustrated through an example from smart grids: the description of a large population of electricity consumers by a parametric distribution gives a nonatomic game with an infinity of different players types, with actions subject to coupling constraints.<br />arXiv admin note: substantial text overlap with arXiv:1806.06230
- Subjects :
- FOS: Computer and information sciences
TheoryofComputation_MISCELLANEOUS
Computer Science::Computer Science and Game Theory
Information Systems and Management
General Computer Science
media_common.quotation_subject
0211 other engineering and technologies
Monotonic function
02 engineering and technology
Management Science and Operations Research
generalized variational inequality
Industrial and Manufacturing Engineering
nonatomic aggregative game
Computer Science - Computer Science and Game Theory
0502 economics and business
Convergence (routing)
FOS: Mathematics
050207 economics
Mathematics - Optimization and Control
Finite set
Parametric statistics
Mathematics
media_common
Sequence
021103 operations research
05 social sciences
ComputingMilieux_PERSONALCOMPUTING
TheoryofComputation_GENERAL
Coupling (probability)
Infinity
Optimization and Control (math.OC)
variational equilibrium
Modeling and Simulation
Variational inequality
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
[INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
coupling aggregative constraints
Mathematical economics
monotone game
Computer Science and Game Theory (cs.GT)
Subjects
Details
- ISSN :
- 03772217
- Volume :
- 301
- Database :
- OpenAIRE
- Journal :
- European Journal of Operational Research
- Accession number :
- edsair.doi.dedup.....ab8473d92c6607f6e90ac7ff30114f5c