### Mathematics in Engineering

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

# Career plans and wage structures: a mean field game approach

• 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.

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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• 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.

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