Career plans and wage structures: a mean field game approach

Benoît Perthame; Edouard Ribes; Delphine Salort; Benoît Perthame; Edouard Ribes; Delphine Salort

doi:10.3934/Mine.2018.1.38

Mathematics in Engineering

2019, Volume 1, Issue 1: 38-54. doi: 10.3934/Mine.2018.1.38

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Research article

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.

Received: 12 May 2018 Accepted: 05 June 2018 Published: 30 August 2018

This paper exemplifies the relationships between career plans and wage structures. It relies on an innovative methodological approach using the mean field games (MFG) theory in a problem of workers management engineering. We describe how an individual can optimize his career in a given structured labor market to come up with an income optimal career trajectory. Similarly, we show that the same thought process can be applied by firms to structure their internal labor market to fit with workers own optimization. Finally, we compute the analytical solutions of our framework and calibrate them to the market data to further our discussion. The interest of the paper relies on the modeling issue and we leave open the complex mathematical questions which range in the field of inverse problems.
- wage structures,
- career optimization,
- mean field games,
- planning problem
Citation: Benoît Perthame, Edouard Ribes, Delphine Salort. Career plans and wage structures: a mean field game approach[J]. Mathematics in Engineering, 2019, 1(1): 38-54. doi: 10.3934/Mine.2018.1.38

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Abstract

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

References

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