SCIENCE CHINA Information Sciences, Volume 59, Issue 5: 052204(2016) https://doi.org/10.1007/s11432-015-5376-9

Stable degree analysis for strategy profiles of evolutionary networked games

More info
  • ReceivedFeb 2, 2015
  • AcceptedApr 8, 2015
  • PublishedApr 8, 2016


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.

Funded by

National Natural Science Foundation of China(61374065)



This work was supported by National Natural Science Foundation of China (Grant No. 61374065) and Research Fund for the Taishan Scholar Project of Shandong Province.


[1] Smith J M, Price G R. Nature, 1973, 246: 15-18 Google Scholar

[2] Hofbauer J, Sigmund K. Bulletin (New Series) American Math Soc, 2003, 40: 479-519 Google Scholar

[3] Szabo G, Fath G. Phys Rep, 2007, 446: 97-216 Google Scholar

[4] Hauert C, Doebeli M. Nature, 2004, 428: 643-646 Google Scholar

[5] Ellison G. Econometrica, 1993, 61: 1047-1071 Google Scholar

[6] Zhang J L, Zhang C Y, Chu T G. Chaos, Solitons Fractals, 2011, 44: 131-136 Google Scholar

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

[8] Bukowski M, Miekisz J. Int J Game Theory, 2004, 33: 41-54 Google Scholar

[9] Taylor P D, Jonker L B. Math Biosci, 1978, 40: 145-156 Google Scholar

[10] Ellison G. Rev Economic Studies, 2000, 67: 17-45 Google Scholar

[11] Balkenborg D, Schlag K H. Int J Game Theory, 2001, 29: 571-595 Google Scholar

[12] Sandholm W H. Theor Econ, 2010, 5: 27-50 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. Google Scholar

[14] Li F F, Sun J T. Automatica, 2011, 47: 2765-2771 Google Scholar

[15] Zhao Y, Li Z Q, Cheng D Z. IEEE Trans Aut Contr, 2011, 56: 1766-1776 Google Scholar

[16] Liu Z B, Wang Y Z. Automatica, 2012, 48: 1839-1844 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. Google Scholar

[18] Feng J E, Yao J, Cui P. Sci China Inf Sci, 2013, 56: 112203-1844 Google Scholar

[19] Zhao Y, Cheng D Z. Sci China Inf Sci, 2014, 57: 012202-1844 Google Scholar

[20] Chen H, Sun J. Automatica, 2014, 50: 1929-1934 Google Scholar

[21] Chen H, Sun J. Neural Netw, 2013, 39: 12-17 Google Scholar

[22] Wang Y Z, Zhang C H, Liu Z B. Automatica, 2012, 48: 1227-1236 Google Scholar

[23] Zhao D W, Peng H P, Li L X, et al. Sci China Inf Sci, 2014, 57: 092114-1236 Google Scholar

[24] Li H T, Wang Y Z. Automatica, 2012, 48: 688-693 Google Scholar

[25] Guo P L, Wang Y Z, Li H T. Automatica, 2013, 49: 3384-3389 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. Control Theory Tech, 2014, 12: 198-214 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. IEEE Trans Automat Contr, 2015, 60: 2402-2415 Google Scholar

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

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号