KTH Mathematics

Probabilistic approach to finite state mean field games A Cecchin, M Fischer arxiv.org/abs/1704.00984 Summary: Finite state mean field games (FSMFG) are defined. The authors aim to prove an approximation result for control-dependent intensity and runnning cost with probabilistic methods. The case of control-dependent intensity was considered in Kolokoltsov (2011). Similar problem were studied in Gomes et al (2013) and Bansra (2014) with ODE/PDE and intensity matrix methods. The problem is relaxed and in the relaxed setting, existence of an optimal feedback control is proven. Under the assumption that the Hamiltonian has a unique minimizer, uniqueness of the optimal feedback is proven. Uniqueness of solution to the FSMFG (the triplet control, state, law) is proven under a monotonicity condition. In a special case of intensity, uniqueness is proven without monotonicity for small time horizons. The approximation result is proven under further assumptions on intensity and running cost. List of papers Front page

Published by: Alexander Aurell Updated: 09-02-2018