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Career plans and wage structures: a mean field game approach

1 Laboratoire Jacques-Louis Lions, Sorbonne Université, UPD, CNRS, Inria, F75005 Paris, France.
2 CERNA, Mines ParisTech, 60 Boulevard Saint-Michel, 75006 Paris, France.
3 Laboratoire de Biologie Computationnelle et Quantitative, Sorbonne Université, CNRS, F75005Paris, France.

This paper exemplifies the relationships between career plans and wage structures. It relieson an innovative methodological approach using the mean field games (MFG) theory in a problem ofworkers management engineering. We describe how an individual can optimize his career in a givenstructured labor market to come up with an income optimal career trajectory. Similarly, we showthat the same thought process can be applied by firms to structure their internal labor market to fit withworkers own optimization. Finally, we compute the analytical solutions of our framework and calibratethem to the market data to further our discussion. The interest of the paper relies on the modeling issueand we leave open the complex mathematical questions which range in the field of inverse problems.
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