Stationary and initial-terminal value problem for collective decision making via mean-field games
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
IEEEJournal
2017 25th Mediterranean Conference on Control and Automation (MED)DOI
10.1109/med.2017.7984269Type
Meetings and ProceedingsLanguage
enISSN
9781509045334EISSN
2473-3504ae974a485f413a2113503eed53cd6c53
10.1109/med.2017.7984269