NDLI: Mean Field (NCE) stochastic control: Populations of major and egoist-altruist agents

Content Provider	IEEE Xplore Digital Library
Author	Kizilkale, A.C. Caines, P.E.
Copyright Year	2011
Description	Author affiliation: Department of Electrical and Computer Engineering and the Centre for Intelligent Machines, McGill University, Montreal, Canada (Kizilkale, A.C.; Caines, P.E.)
Abstract	For noncooperative games the Nash Certainty Equivalence (NCE), or Mean Field (MF) methodology [1], [2] provides decentralized strategies which asymptotically yield Nash equilibria. An extension of this theory to populations of altruistic agents (defined with so-called social cost functions) and to mixed populations was carried out in [3], and a theory treating populations of egoistic agents and one or more so-called major agents was developed in [4]. In this paper we study the equilibria and the overall stability of dynamic LQG games, where (i) there is a single major agent and a large population of mixed minor agents, and (ii) the cost for each minor agent is a convex combination of its own cost and the social cost of the minor agents. We analyse the resulting equilibria, provide experimental results, and present a mean field stochastic control algorithm, which when applied by all agents in the system, gives rise to system behaviour where (i) all agents systems are $L^{2}$ stable, (ii) the set of controls yields an ε-Nash equilibrium for all ε, and (iii) if each minor agent in the system only considers the social cost, then the difference between (i) the cost observed by each minor agent and (ii) the social cost that would be observed if a centralized controller minimizes the social cost tends to zero as the population size grows to infinity.
Starting Page	5547
Ending Page	5552
File Size	463741
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6161425
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Games Trajectory Cost function Equations Limiting Vectors
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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