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