Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Career plans and wage structures: a mean field game approach

1 Laboratoire Jacques-Louis Lions, Sorbonne Universit´e, 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 Universit´e, CNRS, F75005 Paris, France.

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords 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. Mathematics in Engineering, 2018, 1(1): 38-54. doi: 10.3934/Mine.2018.1.38

References

  • 1. Lasry JM and Lions PL (2006) Jeux à champ moyen. I. Le cas stationnaire. CR Math 343: 619–625.
  • 2. Lasry JM and Lions PL (2006) Jeux à champ moyen. II. Horizon fini et contrôle optimal. CR Math 343: 679–684.
  • 3. Lasry JM and Lions PL (2007) Mean field games. Jpn J Math 2: 229–260.    
  • 4. Besoussan A, Frehse J and Yam P (2013) Mean Field Games and Mean Field Type Control Theory, Springer.
  • 5. Gomes D and Sade J (2014) Mean field games models a brief survey. Dyn Games Appl 4: 110–154.    
  • 6. Gueant O, Lasry JM and Lions PL (2011) Mean Field Games and Applications. Springer Berlin Heidelberg, Berlin, Heidelberg, 205–266.
  • 7. Kräkel M and Schöttner A (2012) Internal labor markets and worker rents. Journal of Economic Behavior and Organization 84: 491–509.    
  • 8. Dohmen T (2014) Behavioral labor economics: Advances and future directions. Labour Economics 30: 71–85.    
  • 9. Carmona R, Delarue F and Lacker D (2017) Mean field games of timing and models for bank runs. Appl Math Opt 76: 217–260.    
  • 10. Achdou Y, Buera FJ, Larsy JM, et al. (2014) Partial differential equation models in macroeconomics. Philos T R Soc A 372: 20130397–20130397.    
  • 11. Achdou Y, Giraud PN, Larsy JM, et al. (2016) A long term mathematical model for mining industries. Appl Math Opt 74: 579–618.    
  • 12. Porretta A (2013) On the planning problem for a class of mean field games. CR Math 351: 457– 462.
  • 13. Porretta A (2014) On the planning problem for the mean field games system. Dyn Games Appl 4: 231–256.    
  • 14. Lions PL (2013) Cours au collège de france. Technical report, Collège de France.
  • 15. Doumic M, Perthame B, Ribes E, et al. (2017) Toward an integrated workforce planning framework using structured equations. Eur J Oper Res 262: 217–230.    
  • 16. Perthame B, Ribes E, Salort D, et al. (2017) A model for cost effcient workforce organizational dynamics and its optimization. ArXiv preprint ArXiv:1707.05056.
  • 17. Achdou Y, Camilli F and Capuzzo-Dolcetta I (2013) Mean field games: convergence of a finite difference method. SIAM J Numer Anal 51: 2585–2612.    
  • 18. Achdou Y and Porretta A (2016) Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games. SIAM J Numer Anal 54: 161–186.    
  • 19. Wiatrowski WJ (2013) Employment-based health benefits in small and large private establishments.
  • 20. Abowd JM and Kramarz F (2000) Inter-industry and firm-size wage differentials: New evidence from linked employer-employee data. Technical report, Cornell University.
  • 21. Rogerson R, Shimer R and Wright R (2005) Search-theoretic models of the labor market: A survey. Journal of economic literature 43: 959–988.    
  • 22. Bardi M and Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton- Jacobi-Bellman equations. Birkhäuser Boston.
  • 23. Fleming WH and Soner HM (1993) Controlled Markov Processes and Viscosity Solutions. Vol 25, Springer

 

Reader Comments

your name: *   your email: *  

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved