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Reconstructing a state-independent cost function in a mean-field game model

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arxiv 2402.09297 v2 pith:5CIRSA2F submitted 2024-02-14 math.AP math.OC

Kui Ren , Nathan Soedjak , Kewei Wang , Hongyu Zhai This is my paper · ORCID
classification math.APmath.OC
keywords inversemean-fieldcostfunctiongamesproblemreconstructingstate-independent
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In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a uniqueness result for the inverse problem using the standard multilinearization technique. One of the main features of our work is that we insist that the population distribution be a probability measure, a requirement that is not enforced in some of the existing literature on theoretical inverse mean-field games.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Simultaneously decoding the unknown stationary state and function parameters for mean field games

    math.AP 2025-01 conditional novelty 6.0 of 10

    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.

  2. On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate

    math.AP 2024-12 conditional novelty 6.0 of 10

    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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