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Alexander Aurell: Mean-field control and mean-field type games of BSDEs

Tid: On 2018-10-03 kl 15.15 - 16.15

Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Medverkande: Alexander Aurell (Department of Mathematics, KTH)

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Abstract: The talk will begin with a short background on mean-field control theory and mean-field type games, and how these two problem classes differ from standard stochastic control theory and mean-field games. Then, two recent research projects on the topic, where the state dynamics are specified as backward stochastic differential equations (BSDEs), will be presented. First, we will look at a mean-field control model for motion of pedestrian groups, under the following condition: a target position has to be reached at a certain time in the future. The fixed final destination leads us to a BSDE control problem where distribution-dependent crowd effects like congestion and aversion are present. The optimal crowd control is characterized and behavior in the model is studied by numerical tests. Then, we move on to mean-field type games between two players whose state dynamics are BSDEs. Each player’s goal is to minimize an individual cost functional, that depends on both players’ marginal state distribution. Under some regularity conditions, we can use standard methods to state necessary and sufficient conditions for existence of Nash equilibria.