Kybernetika 60 no. 6, 754-778, 2024

Equilibrium analysis of distributed aggregative game with misinformation

Meng Yuan, Zhaoyang Cheng and Te MaDOI: 10.14736/kyb-2024-6-0754

Abstract:

This paper considers a distributed aggregative game problem for a group of players with misinformation, where each player has a different perception of the game. Player's deception behavior is inevitable in this situation for reducing its own cost. We utilize hypergame to model the above problems and adopt $\epsilon$-Nash equilibrium for hypergame to investigate whether players believe in their own cognition. Additionally, we propose a distributed deceptive algorithm for a player implementing deception and demonstrate the algorithm converges to $\epsilon$-Nash equilibrium for hypergame. % to ensure both cognitive and strategic stability. Further, we provide conditions for the deceptive player to enhance its profit and offer the optimal deceptive strategy at a given tolerance $\epsilon$. Finally, we present the effectiveness of the algorithm through numerical experiments.

Keywords:

distributed aggregative game, deceptive strategy, hypergame, $\epsilon $-Nash equilibrium for hypergame

Classification:

91A10, 68W15, 68W40

paper.pdf

References:

  1. N. Abuzainab and W. Saad: A multiclass mean-field game for thwarting misinformation spread in the internet of battlefield things. IEEE Trans. Commun. 66 (2018), 12, 6643-6658.   DOI:10.1109/TCOMM.2018.2866859
  2. H. Chen, Y. Li, R. H. Louie and B. Vucetic: Autonomous demand side management based on energy consumption scheduling and instantaneous load billing: An aggregative game approach. IEEE Trans. Smart Grid 5 (2014), 4, 1744-1754.   DOI:10.1109/TSG.2014.2311122
  3. J. Chen and Q. Zhu: nterdependent strategic security risk management with bounded rationality in the internet of things. IEEE Trans. Inform. Forensics Security {\mi14} (2019), 11, 2958-2971.   DOI:10.1109/TIFS.2019.2911112
  4. Z. Cheng, G. Chen and Y. Hong: Single-leader-multiple-followers stackelberg security game with hypergame framework. IEEE Trans. Inform. Forensics Security 17 (2022), 954-969.   DOI:10.1109/TIFS.2022.3155294
  5. J. P. Hespanha, Y. S. Ateskan and H. Kizilocak et al.: Deception in non-cooperative games with partial information. In: Proc. 2nd DARPA-JFACC Symposium on Advances in Enterprise Control, Citeseer 2000, pp. 1-9.   CrossRef
  6. S. Huang, J. Lei and Y. Hong: A linearly convergent distributed Nash equilibrium seeking algorithm for aggregative games. IEEE Trans. Automat. Control 68 (2022), 3, 1753-1759.   DOI:10.1109/TAC.2022.3154356
  7. L. Huang and Q. Zhu: Duplicity games for deception design with an application to insider threat mitigation. IEEE Trans. Inform. Forensics Security 16 (2021), 4843-4856.   DOI:10.1109/TIFS.2021.3118886
  8. S. Jelassi, C. Domingo-Enrich, D. Scieur, A. Mensch and J. Bruna: Extragradient with player sampling for faster Nash equilibrium finding. In: Proc. International Conference on Machine Learning 2020.   CrossRef
  9. R. Jin, X. He and H. Dai: On the security-privacy tradeoff in collaborative security: A quantitative information flow game perspective. IEEE Trans. Inform. Forensics Security {\mi14} (2019), 12, 3273-3286.   DOI:10.1109/TIFS.2019.2914358
  10. B. Johansson, T. Keviczky, M. Johansson and K. H. Johansson: Subgradient methods and consensus algorithms for solving convex optimization problems. In: 47th IEEE Conference on Decision and Control, IEEE 2008, pp. 4185-4190.   DOI:10.1109/CDC.2008.4739339
  11. J. Koshal, A. Nedić and U. V. Shanbhag: Distributed algorithms for aggregative games on graphs. Oper. Res. 64 (2016), 3, 680-704.   DOI:10.1287/opre.2016.1501
  12. N. S. Kovach, A. S. Gibson and G. B. Lamont: Hypergame theory: a model for conflict, misperception, and deception. Game Theory (2015).   CrossRef
  13. J. Lei and U. V. Shanbhag: Asynchronous schemes for stochastic and misspecified potential games and nonconvex optimization. Operations Research {|mi 68} (2020), 6, 1742-1766.   DOI:10.1287/opre.2019.1946
  14. S. Liang, P. Yi, Y. Hong and K. Peng: Exponentially convergent distributed Nash equilibrium seeking for constrained aggregative games. Autonomous Intell. Systems 2 (2022), 1, 6.   DOI:10.1155/2022/1036942
  15. J. Ma, Z. Yang and Z. Chen: Distributed Nash equilibrium tracking via the alternating direction method of multipliers. Kybernetika 59 (2023), 4, 612-632.   DOI:10.14736/kyb-2023-4-0612
  16. Y. Meng, M. Broom and A. Li: Impact of misinformation in the evolution of collective cooperation on networks. J. Royal Soc. Interface 20 (2023), 206, 20230295.   DOI:10.1098/rsif.2023.0295
  17. Y. Meng, S. P. Cornelius, Y. Y. Liu and A. Li: Dynamics of collective cooperation under personalised strategy updates. Nature Commun. 15 (2024), 1, 3125.   DOI:10.56337/sbm.1350842
  18. A. Nedic, A. Ozdaglar and P. A. Parrilo: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Automat. Control 55 (2010), 4, 922-938.   DOI:10.1109/TAC.2010.2041686
  19. K. C. Nguyen, T. Alpcan and T. Basar: Security games with incomplete information. In: 2009 IEEE International Conference on Communications, pp. 1-6.   DOI:10.1109/icc.2009.5199443
  20. D. Paccagnan, B. Gentile, F. Parise, M. Kamgarpour and J. Lygeros: Distributed computation of generalized Nash equilibria in quadratic aggregative games with affine coupling constraints. In: 55th IEEE Conference on Decision and Control, IEEE 2016, pp. 6123-6128.   DOI:10.1109/cdc.2016.7799210
  21. D. Paccagnan, B. Gentile, F. Parise, M. Kamgarpour and J. Lygeros: Nash and wardrop equilibria in aggregative games with coupling constraints. IEEE Trans. Automat. Control 64 (2018), 4, 1373-1388.   DOI:10.1109/TAC.2018.2849946
  22. J. Pawlick, E. Colbert and Q. Zhu: Modeling and analysis of leaky deception using signaling games with evidence. IEEE Trans. Inform. Forensics Security 14 (2018), 7, 1871-1886.   DOI:10.1109/TIFS.2018.2886472
  23. Y. Sasaki: Preservation of misperceptions-stability analysis of hypergames. In: Proc. 52nd Annual Meeting of the ISSS-2008, Madison 2008.   CrossRef
  24. Y. Sasaki: Generalized Nash equilibrium with stable belief hierarchies in static games with unawareness. Ann. Oper. Res. 256 (2017), 271-284.   DOI:10.1007/s10479-016-2266-5
  25. G. Scutari, D. P. Palomar, F. Facchinei and J.-S. Pang: Convex optimization, game theory, and variational inequality theory. IEEE Signal Process. Magazine 27 (2010), 3, 35-49.   DOI:10.1109/MSP.2010.936021
  26. M. Wang, K. W. Hipel and N. M. Fraser: Modeling misperceptions in games. Behavioral Sci. 33 (1988), 3, 207-223.   DOI:10.1002/bs.3830330305
  27. J. Wang, J. F. Zhang and X. He: Differentially private distributed algorithms for stochastic aggregative games. Automatica 142 (2022), 110440.   DOI:10.1016/j.automatica.2022.110440
  28. G. Xu, G. Chen, H. Qi and Y. Hong: Efficient algorithm for approximating Nash equilibrium of distributed aggregative games. IEEE Trans. Cybernet. 53 (2023), 7, 4375-4387.   DOI:10.1109/TCYB.2022.3175831
  29. T. Yilmaz and Ö. Ulusoy: Misinformation propagation in online social networks: game theoretic and reinforcement learning approaches. IEEE Trans. Comput. Social Systems (2022).   DOI:10.1109/tcss.2022.3208793
  30. S. Yu, Q. Sun and Z. Yang: Recent advances on false information governance. Control Theory Technol. 21 (2023), 1, 110-113.   DOI:10.1007/s11768-023-00126-1
  31. H. Zhang, H. Qin and G. Chen: Bayesian Nash equilibrium seeking for multi-agent incomplete-information aggregative games. Kybernetika (2023), 575-591, 09 2023.   DOI:10.14736/kyb-2023-4-0575
  32. T. Y. Zhang and D. Ye: False data injection attacks with complete stealthiness in cyber-physical systems: A self-generated approach. Automatica 120 (2020), 109117.   DOI:10.1016/j.automatica.2020.109117