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

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Stella, Leonardo and Bauso, Dario 2017. Stationary and initial-terminal value problem for collective decision making via mean-field games. IEEE. https://doi.org/10.1109/med.2017.7984269
AuthorsStella, Leonardo and Bauso, Dario
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.

KeywordsGames, Mathematical model, Markov processes, Sociology, Statistics, Microscopy, Robustness
Year2017
Journal2017 25th Mediterranean Conference on Control and Automation (MED)
2017 25th Mediterranean Conference on Control and Automation (MED)
PublisherIEEE
ISSN9781509045334
2473-3504
Digital Object Identifier (DOI)https://doi.org/10.1109/med.2017.7984269
Web address (URL)http://hdl.handle.net/10545/624663
hdl:10545/624663
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Open
Publication datesJul 2017
Publication process dates
Deposited06 Apr 2020, 09:08
Accepted2017
ContributorsUniversity of Sheffield
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