Semi-tensor product approach to networked evolutionary games

J. von Neumann. Zur theorie der gesellschaftsspiele. Mathematische Annalen, 1928, 100(1): 295–320.

J. von Neumann, O. Morgenstern. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944.

J. Nash. Non-cooperative game. The Annals of Mathematics, 1951, 54(2): 286–295.

D. Gale, L. S. Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 1962, 69(1): 9–15.

D. Monderer, L. S. Shapley. Potential games. Games and Economic Behavior, 1996, 14(1): 124–143.

P. D. Taylor, L. B. Jonker. Evolutionary stable strategies and game dynamics. Mathematical Biosciences, 1978, 40(1/2): 145–156.

E. L. Charnov. The Theory of Sex Allocation. Princeton: Princiton University Press, 1982.

R. Sugden. The Economics of Rights, Cooperation and Welfre. Oxford: Blackwwell, 1986.

H. Ohtsuki, C. Hauert, E. Lieberman, et al. A simple rule for the evolution of cooperation on graphs and social networks. Nature, 2006, 441(7092): 502–505.

M. A. Nowak, R. M. May. Evolutionary games and spatial chaos. Nature, 1992, 359(6357): 826–829.

G. Szabo, C. Toke. Evolutionary prisoner’s dilemma game on a square lattice. Physical Review E, 1998, 58(1): 69–73.

F. C. Santos, M. D. Santos, J. M. Pacheco. Social diversity promotes the emergence of cooperation in public goods games. Nature, 2008, 454(7201): 213–216.

L. Wang, F. Fu, X. Chen, et al. Evolutionary games on complex networks. CAAI Transactions on Intelligent Systems, 2007, 2(2): 1–9 (in Chinese).

X. Wang, X. Li, G. Chen. Network Science: An Introduction. Beijing: Higher Education Press, 2012 (in Chinese).

Z. Rong, M. Tang, X. Wang, et al. A survey on 2012 complex networks. Journal of University of Science and Technology of China, 2012, 41(6): 801–80

D. Cheng, H. Qi, Z. Li. Analysis and Control of Boolean Networks: A Semi-tensor Product Approach. London: Springer, 2011.

D. Cheng, H. Qi, Y. Zhao. An Introduction to Semi-tensor Product of Matrices and Its Applications. Singapore: World Scientific, 2012.

D. Cheng, H. Qi, Y. Zhao. Analysis and control of general logical networks — An algebraic approach. Annual Reviews in Control, 2012, 36(1): 11–25.

E. Fornasini, M. E. Valcher. On the periodic trajectories of Boolean control networks. Automatica, 2013: 49(5): 1506–1509.

E. Fornasini, M. E. Valcher. Observability, reconstructibility and state observers of Boolean control networks. IEEE Transactions on Automatic Control, 2013, 58(6): 1390–1401.

G. Hochma, M. Margaliot, E. Fornasini, et al. Symbolic dynamics of Boolean control networks. Automatica, 2013, 49(8): 2525–2530.

D. Laschov, M. Margaliot. Controllability of Boolean control networks via the Perron-Frobenius theory. Automatica, 2012, 48(6): 1218–1223.

F. Li, J. Sun. Controllability of Boolean control networks with time delays in states. Automatica, 2011, 47(3): 603–607.

F. Li, J. Sun. Controllability of probabilistic Boolean control networks. Automatica, 2011, 47(12): 2765–2771.

H. Li, Y. Wang. Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method. Automatica, 2012, 48(4): 688–693.

L. Zhang, K. Zhang. L 2 stability, H∞ control of switched homogeneous nonlinear systems and their semi-tensor product of matrices representation. International Journal of Robust and Nonlinear Control, 2013, 23(6): 638–652.

Y. Zhao, Z. Li, D. Cheng. Optimal control of logical control networks. IEEE Transactions on Automatic Control, 2011, 56(8): 1766–1776.

R. Li, M. Yang, T. Chu. State feedback stabilization for Boolean control networks. IEEE Transactions on Automatic Control, 2013, 58(7): 1853–1857.

Z. Liu, Y. Wang. Disturbance decoupling of mix-valued logical networks via the semi-tensor product method. Automatica, 2012, 48(8): 1839–1844.

M. Yang, R. Li, T. Chu. Controller design for disturbance decoupling of Boolean control networks. Automatica, 2013, 49(1): 273–277.

Y. Zhao, J. Kim, M. Filippone. Aggregation algorithm towards large-scale Boolean network analysis. IEEE Transactions on Automatic Control, 2013, 58(8): 1976–1985.

R. Li, M. Yang, T. Chu. Synchronization design of Boolean networks via the semi-tensor product method. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(6): 996–1001.

Y. Wang, C. Zhang, Z. Liu. A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems. Automatica, 2012, 48(7): 1227–1236.

X. Xu, Y. Hong. Matrix approach to model matching of asynchrollous sequential machines. IEEE Transactions on Automatic Control, 2013, 58(11): 2974–2979.

D. Cheng, X. Xu. Bi-decomposition of multi-valued logical functions and its applications. Automatica, 2013, 49(7): 1979–1985.

D. Cheng, F. He, H. Qi, et al. Modeling, analysis and control of networked evolutionary games. IEEE Transactions on Automatic Control, provitionary accepted: http://lsc.amss.ac.cn/~dcheng/preprint/NTGAME02.pdf .

D. Cheng, T. Xu, H. Qi. Evolutionarily stable strategy of networked evolutionarily games. IEEE Transactions on Neural Networks and Learning Systems: DOI 10.1109/TNNLS.2013.2293149.

D. Cheng. On finite potential game. Automatica, accepted: http://lsc.amss.ac.cn/~dcheng/preprint/FPG2014.pdf .

L. Ljung. T. Söberström. Theory and Practice of Recursive Identification. Cambridge: The MIT Press, 1982.

E. Rasmusen. Games and Information: An Introduction to Game Theory. 4th ed. Oxford: Basil Blackwell, 2007.

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

J. P. Benoit, V. Krishna. Finitely repeated games. Econometrica, 1985, 17(4): 317–320.

A. Traulsen, M. A. Nowak, J. M. Pacheco. Stochastic dynamics of invasion and fixation. Physical Review E, 2006, 74(1): DOI 10.1103/PhysRevE.74.011909.

H. P. Young. The evolution of conventions. Econometrica, 1993, 61(1): 57–84.

C. Berge. Graphs and Hypergraphs. Translated by E. Minieka, London: North-Hollabd Pub., 1973.

D. Monderer, L. S. Shapley. Fictitious play property for games with identical interests. Journal of Economic Theory, 1996, 68(1): 258–265.

H. Qi, D. Cheng, H. Dong. On networked evolutionary games — Part 1: formulation. Proceedings of the 19th IFAC World Congress. South Africa: Cape Town, 2014: http://lsc.amss.ac.cn/~dcheng/preprint/IFAC2014-NEG-part1.pdf .

D. Cheng, F. He, T. Xu. On networked evolutionary games — Part 2: dynamics and control. Proceedings of the 19th IFAC World Congress. South Africa: Cape Town, 2014: http://lsc.amss.ac.cn/~dcheng/preprint/IFAC2014-NEG-part2.pdf .