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Steering the Distribution of Agents in Mean-Field Games System

Author

Listed:
  • Yongxin Chen

    (Iowa State University)

  • Tryphon T. Georgiou

    (University of California)

  • Michele Pavon

    (Università di Padova)

Abstract

The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. This is formulated as a mean-field game problem, and is discussed in both non-cooperative games and cooperative games settings. In the non-cooperative games setting, a terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. In the cooperative games setting, the goal is to find a common optimal control that would drive the distribution of the agents to a targeted one. We focus on the cases when the underlying dynamics is linear and the running cost is quadratic. Our approach relies on and extends the theory of optimal mass transport and its generalizations.

Suggested Citation

  • Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2018. "Steering the Distribution of Agents in Mean-Field Games System," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 332-357, October.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1365-7
    DOI: 10.1007/s10957-018-1365-7
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    References listed on IDEAS

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    1. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    3. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    4. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    5. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2016. "On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 671-691, May.
    6. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
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    8. Alessio Porretta, 2014. "On the Planning Problem for the Mean Field Games System," Dynamic Games and Applications, Springer, vol. 4(2), pages 231-256, June.
    9. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
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