Skip to main content
Log in

Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme

  • Research article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

In this paper, a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks, where the two subnetworks have opposite payoff function. A novel distributed projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the process of computing Nash equilibrium. In our algorithm, each agent is determined by an independent identically distributed Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus estimate, it effectively reduces the amount of computation and calculation time. Moreover, the traditional assumption of stepsize adopted in the existing methods is removed, and the stepsizes in our algorithm are randomized diminishing. Besides, we prove that all agents converge to Nash equilibrium with probability 1 by our algorithm. Finally, a simulation example verifies the validity of our algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Ghaderi, J., & Srikant, R. (2014). Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate. Automatica, 50, 3209–3215.

    Article  MathSciNet  Google Scholar 

  2. Ardagna, D., Ciavotta, M., & Passacantando, M. (2017). Generalized Nash equilibria for the service provisioning problem in multi-cloud systems. IEEE Transactions on Services Computing, 10(3), 381–395.

    Article  Google Scholar 

  3. Ye, M., & Hu, G. (2017). Game design and analysis for price based demand response: An aggregate game approach. IEEE Transactions on Cybernetics, 47(3), 720–730.

    Article  Google Scholar 

  4. Yi, P., & Pavel, L. (2019). An operator splitting approach for distributed generalized Nash equilibria computation. Automatica, 102, 111–121.

    Article  MathSciNet  Google Scholar 

  5. Ye, M., & Hu, G. (2017). Distributed Nash equilibrium seeking by a consensus based approach. IEEE Transactions on Automatic Control, 62(9), 4811–4818.

    Article  MathSciNet  Google Scholar 

  6. Deng, Z., & Nian, X. (2019). Distributed generalized Nash equilibrium seeking algorithm design for aggregative games over weight-balanced digraphs. IEEE Transactions on Neural Networks and Learning Systems, 30(3), 695–706.

    Article  MathSciNet  Google Scholar 

  7. Liang, S., Yi, P., & Hong, Y. (2017). Distributed Nash equilibrium seeking for aggregative games with coupled constraints. Automatica, 85, 179–185.

    Article  MathSciNet  Google Scholar 

  8. Shi, C., & Yang, G. (2019). Distributed Nash equilibrium computation in aggregative games: An event-triggered algorithm. Information Sciences, 489, 289–302.

    Article  MathSciNet  Google Scholar 

  9. Zeng, X., Chen, J., Liang, S., & Hong, Y. (2019). Generalized Nash equilibrium seeking strategy for distributed nonsmooth multi-cluster game. Automatica, 103, 20–26.

    Article  MathSciNet  Google Scholar 

  10. Mcdonald, C., Alajaji, F., & Yksel, S. (2020). Two-way Gaussian networks with a jammer and decentralized control. IEEE Transactions on Control of Network Systems, 7(1), 446–457.

    Article  MathSciNet  Google Scholar 

  11. Vamvoudakis, K.G., Hespanha, J.P., Sinopoli, B. & Mo, Y. (2012). Adversarial detection as a zero-sum game. In: IEEE 51th Annual Conference on Decision and Control, HI, pp. 7133–7138.

  12. Gharesifard, B., & Cortes, J. (2013). Distributed convergence to Nash equilibria in two-network zero-sum games. Automatica, 49(6), 1683–1692.

    Article  MathSciNet  Google Scholar 

  13. Lou, Y., Hong, Y., Xie, L., Shi, G., & Johansson, K.-H. (2016). Nash equilibrium computation in subnetwork zero-sum games with switching communications. IEEE Transactions on Automatic Control, 61(10), 2920–2935.

    Article  MathSciNet  Google Scholar 

  14. Shi, C., & Yang, G. (2019). Nash equilibrium computation in two-network zero-sum games: An incremental algorithm. Neurocomputing, 359, 114–121.

    Article  Google Scholar 

  15. Peng, Y., & Hong, Y. (2015). Stochastic sub-gradient algorithm for distributed optimization with random sleep scheme. Control Theory and Technology, 13(4), 333–347.

    Article  MathSciNet  Google Scholar 

  16. Li, H., Wang, Z., Xia, D., & Han, Q. (2019). Random sleep scheme-based distributed optimization algorithm over unbalanced time-varying networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2019.2945864.

    Article  Google Scholar 

  17. Shi, C., & Yang, G. (2019). Multi-cluster distributed optimization via random sleep strategy. Journal of the Franklin Institute, 356(10), 5353–5377.

    Article  MathSciNet  Google Scholar 

  18. Zhu, M., & Frazzoli, E. (2016). Distributed robust adaptive equilibrium computation for generalized convex games. Automatica, 63, 82–91.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaohong Nian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiong, H., Han, J., Nian, X. et al. Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme. Control Theory Technol. 19, 405–417 (2021). https://doi.org/10.1007/s11768-021-00055-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-021-00055-x

Keywords

Navigation