Skip to main content
SpringerLink
Log in

Stable degree analysis for strategy profiles of evolutionary networked games

网络演化博弈中策略组合的稳定度分析

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this paper, we investigate the stable degree of strategy profile for evolutionary networked games by using the semi-tensor product method, and present a number of new results. First, we propose the concept of k-degree stability for strategy profiles based on a normal evolutionary networked game model. Second, using the semi-tensor product of matrices, we convert the game dynamics with “best imitate” strategy updating rule into an algebraic form. Third, based on the algebraic form of the game, we analyzed the stable degree of strategy profile, and proposed two necessary and sufficient conditions for the k-degree stability of strategy profile. Furthermore, we discuss the computation problem of the transient time within which a disturbed strategy profile can be restored, and also establish an algorithm for the verification of the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained in this paper are very effective.

摘要

创新点

基于矩阵半张量积这一新工具,本文研究了有限网络演化博弈中策略组合的稳定度分析问题。 主要创新在于: (1) 提出了玩家策略组合的 k 度稳定性的概念, (2) 针对最优模仿策略调整规则, 为博弈的演化过程建立一个严格的动力学方程, 并将其转化为代数形式, (3) 得到了策略组合 k 度稳定的两个充分必要条件, 在 MATLAB 的帮助下这些条件都是很容易验证的, 并且给出一个计算策略组合稳定度的算法。

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Smith J M, Price G R. The logic of animal conflict. Nature, 1973; 246: 15–18

    Article  Google Scholar 

  2. Hofbauer J, Sigmund K. Evolutionary game dynamics. Bulletin (New Series) American Math Soc, 2003; 40: 479–519

    Article  MathSciNet  MATH  Google Scholar 

  3. Szabo G, Fath G. Evolutionary games on graphs. Phys Rep, 2007; 446: 97–216

    Article  MathSciNet  Google Scholar 

  4. Hauert C, Doebeli M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature, 2004; 428: 643–646

    Article  Google Scholar 

  5. Ellison G. Learning, local interaction, and coordination. Econometrica, 1993; 61: 1047–1071

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhang J L, Zhang C Y, Chu T G. The evolution of cooperation in spatial groups. Chaos, Solitons Fractals, 2011; 44: 131–136

    Article  MathSciNet  Google Scholar 

  7. Smith J M. Evolution and the Theory of Games. Cambridge: Cambridge University Press, 1982

    Book  MATH  Google Scholar 

  8. Bukowski M, Miekisz J. Evolutionary and asymptotic stability in symmetric multi-player games. Int J Game Theory, 2004; 33: 41–54

    Article  MathSciNet  MATH  Google Scholar 

  9. Taylor P D, Jonker L B. Evolutionary stable strategies and game dynamics. Math Biosci, 1978; 40: 145–156

    Article  MathSciNet  MATH  Google Scholar 

  10. Ellison G. Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution. Rev Economic Studies, 2000; 67: 17–45

    Article  MathSciNet  MATH  Google Scholar 

  11. Balkenborg D, Schlag K H. Evolutionarily stable set. Int J Game Theory, 2001; 29: 571–595

    Article  MathSciNet  MATH  Google Scholar 

  12. Sandholm W H. Local stability under evolutionary game dynamics. Theor Econ, 2010; 5: 27–50

    Article  MathSciNet  MATH  Google Scholar 

  13. Cheng D Z, Qi H S, Li Z Q. Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach. London: Springer-Verlag, 2011

    Book  MATH  Google Scholar 

  14. Li F F, Sun J T. Controllability of probabilistic Boolean control networks. Automatica, 2011; 47: 2765–2771

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhao Y, Li Z Q, Cheng D Z. Optimal control of logical control network. IEEE Trans Aut Contr, 2011; 56: 1766–1776

    Article  MathSciNet  Google Scholar 

  16. Liu Z B, Wang Y Z. Disturbance decoupling of mix-valued logical networks via the semi-tensor product method. Automatica, 2012; 48: 1839–1844

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu Z B, Wang Y Z, Li H T. Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks. Sci China Inf Sci, 2014, 57, 052201

    MathSciNet  MATH  Google Scholar 

  18. Feng J E, Yao J, Cui P. Singular Boolean networks: semi-tensor product approach. Sci China Inf Sci, 2013, 56: 112203

    Article  MathSciNet  Google Scholar 

  19. Zhao Y, Cheng D Z. On controllability and stabilizability of probabilistic Boolean control networks. Sci China Inf Sci, 2014, 57: 012202

    MathSciNet  MATH  Google Scholar 

  20. Chen H, Sun J. Output controllability and optimal output control of state-dependent switched Boolean control networks. Automatica, 2014; 50: 1929–1934

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen H, Sun J. A new approach for global controllability of higher order Boolean control network. Neural Netw, 2013; 39: 12–17

    Article  MATH  Google Scholar 

  22. Wang Y Z, Zhang C H, Liu Z B. A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems. Automatica, 2012; 48: 1227–1236

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhao D W, Peng H P, Li L X, et al. Novel way to research nonlinear feedback shift register. Sci China Inf Sci, 2014, 57: 092114

    MathSciNet  Google Scholar 

  24. Li H T, Wang Y Z. Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method. Automatica, 2012; 48: 688–693

    Article  MathSciNet  MATH  Google Scholar 

  25. Guo P L, Wang Y Z, Li H T. Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method. Automatica, 2013; 49: 3384–3389

    Article  MathSciNet  MATH  Google Scholar 

  26. Cheng D Z, Zhao Y, Mu Y. Strategy optimization with its application to dynamic games. In: Proceedings of 49th IEEE Conference on Decision and Control, Atlanta, 2010. 5822–5827

    Google Scholar 

  27. Cheng D Z, Qi H S, He F, et al. Semi-tensor product approach to networked evolutionary games. Control Theory Tech, 2014; 12: 198–214

    Article  MathSciNet  MATH  Google Scholar 

  28. Cheng D Z, Xu T. Application of STP to cooperative games. In: Proceedings of 10th IEEE International Conference on Control and Automation, Zhejiang, 2013. 1680–1685

    Google Scholar 

  29. Cheng D Z, He F H, Qi H S, et al. Modeling, analysis and control of networked evolutionary games. IEEE Trans Automat Contr, 2015; 60: 2402–2415

    Article  MathSciNet  Google Scholar 

  30. Skyrms B. The Stag Hunt and the Evolution of Social Structure. Cambridge: Cambridge University Press, 2004

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Peilian Guo, Yuzhen Wang & Haitao Li

  2. Department of Mathematics, Shandong Normal University, Jinan, 250014, China

    Haitao Li

Authors
  1. Peilian Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuzhen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haitao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuzhen Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, P., Wang, Y. & Li, H. Stable degree analysis for strategy profiles of evolutionary networked games. Sci. China Inf. Sci. 59, 052204 (2016). https://doi.org/10.1007/s11432-015-5376-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-015-5376-9

Keywords

关键词

Search

Navigation