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    Stationary and initial-terminal value problem for collective decision making via mean-field games

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    Authors
    Stella, Leonardo
    Bauso, Dario
    Affiliation
    University of Sheffield
    Issue Date
    2017-07
    
    Metadata
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    Abstract
    Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, following some optimality criteria. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, thus introducing mean-field terms in the running and the terminal cost. The first contribution is a mean-field model that takes into account the macroscopic and the microscopic dynamics. The second contribution is the study of the mean-field equilibrium resulting from solving the initial-terminal value problem, involving the Kolmogorov equations and the Hamilton-Jacobi ODEs. The third contribution is the analysis of a stationary equilibrium for the system, which can be obtained in the asymptotic limit from the nonstationary equilibrium. We reframe our analysis within the context of Lyapunov's linearisation method and stability theory of nonlinear systems.
    Citation
    Stella, L. and Bauso, D., (2017). 'Stationary and initial-terminal value problem for collective decision making via mean-field games'. New York: IEEE 25th Mediterranean Conference on Control and Automation (MED), Valetta, Malta, 3-6 July 2017. New York: IEEE, pp. 1125-1130.
    Publisher
    IEEE
    Journal
    2017 25th Mediterranean Conference on Control and Automation (MED)
    URI
    http://hdl.handle.net/10545/624663
    DOI
    10.1109/med.2017.7984269
    Additional Links
    https://ieeexplore.ieee.org/abstract/document/7984269/keywords#keywords
    Type
    Meetings and Proceedings
    Language
    en
    ISSN
    9781509045334
    EISSN
    2473-3504
    ae974a485f413a2113503eed53cd6c53
    10.1109/med.2017.7984269
    Scopus Count
    Collections
    Department of Electronics, Computing & Maths

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