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Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

Author

Listed:
  • Fabio Bagagiolo

    (University of Trento)

  • Dario Bauso

    (University of Sheffield)

  • Rosario Maggistro

    (University of Trento)

  • Marta Zoppello

    (University of Trento)

Abstract

This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is illustrated via numerical studies.

Suggested Citation

  • Fabio Bagagiolo & Dario Bauso & Rosario Maggistro & Marta Zoppello, 2017. "Game Theoretic Decentralized Feedback Controls in Markov Jump Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 704-726, May.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-017-1078-3
    DOI: 10.1007/s10957-017-1078-3
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    References listed on IDEAS

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    1. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    3. Fabio Bagagiolo & Dario Bauso, 2014. "Mean-Field Games and Dynamic Demand Management in Power Grids," Dynamic Games and Applications, Springer, vol. 4(2), pages 155-176, June.
    4. repec:dau:papers:123456789/3001 is not listed on IDEAS
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    6. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    7. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
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    Cited by:

    1. Fabio Bagagiolo & Silvia Faggian & Rosario Maggistro & Raffaele Pesenti, 2022. "Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists’ Flow Model," Networks and Spatial Economics, Springer, vol. 22(2), pages 243-266, June.

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