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.


    The rapid development of science, technology, and engineering, and their central role in our society, are often intrinsically correlated with the deep understanding and high-quality applications of advanced mathematics. Science, technology, engineering, and mathematics are united in the popular acronym STEM, and in fact we believe that the mutual support between all the disciplines related to mathematics and engineering can play the role of a solid "stem" sustaining the growing petals of our ever-changing society.

    This interplay between engineering and mathematics occurs at different levels, such as the process of formalizing, testing, and confirming models that describe complex phenomena, the analysis of data, the quantitative characterization of patterns arising in nature, the precise prediction of events partially governed by chance, the invention of codes and algorithms for fruitful interactions between humans and machines, the establishment of coherent frameworks for strategic decision making - just to name a few scenarios.

    We found therefore the need to provide an inclusive forum to allow for an open dialogue across disciplinary boundaries, focused on top quality mathematics and engineering, which overcomes the rigid distinction between "pure" and "applied" mathematics, so that scientists and mathematicians can discuss and corroborate mathematical theories and methods in view of their applications in engineering.

    Mathematics in Engineering is indeed an interdisciplinary journal focused on high-quality applications of mathematics to science and engineering. The journal publishes innovative articles with solid theoretical foundations and concrete applications, after a rigorous peer-review process.

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    The mathematical methodologies include numerical analysis, differential equations, calculus of variations, dynamical systems, statistical mechanics, deterministic and stochastic models.

    To achieve the highest standards, we have invited many world leading researchers to take part in the Editorial Board: we are very indebted to them for their availability and we are sure that they will be the cornerstone towards the success of the journal.

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    Editors-in-Chief



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