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Unique determination of cost functions in a multipopulation mean field game model
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This paper studies an inverse problem for a multipopulation mean field game (MFG) system where the objective is to reconstruct the running and terminal cost functions of the system that couples the dynamics of different populations. We derive uniqueness results for the inverse problem with different types of available data. In particular, we show that it is possible to uniquely reconstruct some simplified forms of the cost functions from data measured only on a single population component under mild additional assumptions on the coupling mechanism. The proofs are based on the standard multilinearization technique that allows us to reduce the inverse problems into simplified forms.
Forward citations
Cited by 2 Pith papers
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Simultaneously decoding the unknown stationary state and function parameters for mean field games
Under restrictive admissibility conditions, a quadratic time-dependent mean field game is uniquely identifiable from full lateral boundary Cauchy data of its perturbed stationary states.
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On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate
Two new Carleman estimates yield Lipschitz and Hölder stability and an inverse-source uniqueness theorem for coupled stochastic mean field game equations with common noise.
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