For mean field games with double-integrator dynamics, existence of weak solutions and a flow representation of the population density are proved despite a non-coercive Hamiltonian.
Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system
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abstract
Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the so-called Mean Field Game system with state constraints. For this, we show a global semiconvavity property of the value function associated with optimal control problems with state constraints.
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math.AP 1years
2019 1verdicts
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Deterministic mean field games with control on the acceleration
For mean field games with double-integrator dynamics, existence of weak solutions and a flow representation of the population density are proved despite a non-coercive Hamiltonian.