TY  - GEN
AB  - We study mean field games with scalar Itô-type dynamics and costs that are
submodular with respect to a suitable order relation on the state and measure space. The
submodularity assumption has a number of interesting consequences. Firstly, it allows us to
prove existence of solutions via an application of Tarski's fixed point theorem, covering cases
with discontinuous dependence on the measure variable. Secondly, it ensures that the set
of solutions enjoys a lattice structure: in particular, there exist a minimal and a maximal
solution. Thirdly, it guarantees that those two solutions can be obtained through a simple
learning procedure based on the iterations of the best-response-map. The mean field game
is first defined over ordinary stochastic controls, then extended to relaxed controls. Our
approach allows also to treat a class of submodular mean field games with common noise in
which the representative player at equilibrium interacts with the (conditional) mean of its
state's distribution.
DA  - 2019
KW  - Mean field games
KW  - submodular cost function
KW  - complete lattice
KW  - first order stochastic dominance
KW  - Tarski's fixed point theorem.
LA  - eng
PY  - 2019
SN  - 0931-6558
TI  - Submodular Mean Field Games. Existence and Approximation of Solutions
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29366991
Y2  - 2024-11-22T05:35:01
ER  -