Browsing by Author "FRIHI, Zahrate El Oula"

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    Control of hierarchical mean field type games
    (Université Badji Mokhtar Annaba, 2024) FRIHI, Zahrate El Oula
    This thesis focuses on solving hierarchical leadership mean-feld-type games with jump difusion state equations and two diferent performing functionals using two diferent methods, concluding with a numerical analysis of the impact of the hierarchy on the fnal solution. In Paper A, we provide a solution for a hierarchical mean-feld type optimal control problem with polynomial performing functional in three forms using the dynamic rogramming principle method. The frst form is a one-level mean- feld type game when the player acts simultaneously without information diferences. The second form is a Stackelberg mean feld type game, where the players are divided into two groups in two levels, one acting frst, then the other reacting. The last case is a fully hierarchical mean-feld type game when the number of hierarchy levels is equal to the number of players. Numerical investigation proves the existence of a signifcant efect of the hierarchy form on the optimal performing functional. In paper B, we are interested in the hierarchical mean-feld type optimal control problem of electricity production in a smart grid energy market composed of n − 1 prosumers with n ≥ 2 and one major producer, the market leader. These n agents impose their production strategies sequentially in a hierarchal order. The market leader is at the top of the hierarchy, and the other prosumers follow him at separate levels according to their production capacity. We model the problem by a jump-difusion stochastic diferential state equation and a quadratic cost functional. The solution is established using the direct method, and two numerical scenarios are considered.