A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 1 Issue 1
Jan.  2014

IEEE/CAA Journal of Automatica Sinica

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Daizhan Cheng, Tingting Xu, Fenghua He and Hongsheng Qi, "On Dynamics and Nash Equilibriums of Networked Games," IEEE/CAA J. of Autom. Sinica, vol. 1, no. 1, pp. 10-18, 2014.
Citation: Daizhan Cheng, Tingting Xu, Fenghua He and Hongsheng Qi, "On Dynamics and Nash Equilibriums of Networked Games," IEEE/CAA J. of Autom. Sinica, vol. 1, no. 1, pp. 10-18, 2014.

On Dynamics and Nash Equilibriums of Networked Games

Funds:

This work was supported by National Natural Science Foundation of China (61074114, 61273013, 61104065, 61333001).

  • Networked noncooperative games are investigated, where each player (or agent) plays with all other players in its neighborhood. Assume the evolution is based on the fact that each player uses its neighbors' current information to decide its next strategy. By using sub-neighborhood, the dynamics of the evolution is obtained. Then a method for calculating Nash equilibriums from mixed strategies of multi-players is proposed. The relationship between local Nash equilibriums based on individual neighborhoods and global Nash equilibriums of overall network is revealed. Then a technique is proposed to construct Nash equilibriums of an evolutionary game from its one step static Nash equilibriums. The basic tool of this approach is the semi-tensor product of matrices, which converts strategies into logical matrices and payoffs into pseudo-Boolean functions, then networked evolutionary games become discrete time dynamic systems.

     

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  • [1]
    Axelrod R. The Evolution of Cooperation. New York:Basic Books, 1984
    [2]
    Smith J M, Price G R. The logic of animal conflict. Nature, 1973, 246(5427):15-18
    [3]
    Holme P, Saramäki J. Temporal networks. Physics Reports, 2013, 519(3):97-125
    [4]
    Lv L, Medo M, Yeung C H, Zhang Y C, Zhang Z K, Zhou T. Recommender systems. Physics Reports, 2012, 519(1):1-49
    [5]
    Bilbao J M. Cooperative Games on Combinatorial Structures. Boston:Kluwer Acadmic Publisher, 2000
    [6]
    Branzei R, Dimitrov D, Tijs S. Models in Cooperative Game Theory (2nd edition). Berlin:Springer-Verlag, 2008
    [7]
    Hauert C, Doebeli M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature, 2004, 428:643-646
    [8]
    Nowak M A, May R M. Evolutionary games and spatial chaos. Nature, 1992, 359(6398):826-829
    [9]
    Santos F C, Santos M D, Pacheco J M. Social diversity promotes the emergence of cooperation in public goods games. Nature, 2008, 454(7201):213-216
    [10]
    Rong Zhi-Hai, Tang Ming, Wang Xiao-Fan, Wu Zhi-Xi, Yan Gang, Zhou Tiao. Survey on complex networks. Journal of University of Electronic Science and Technology of China, 2012, 41(6):801-807(in Chinese)
    [11]
    Wang Long, Fu Feng, Chen Xiao-Jie, Wang Jing, Li Zhuo-Zheng, Xie Guang-Ming, Chu Tian-Guang. Evolutionary games on complex networks. CAAI Transactions on Intelligent Systems, 2007, 2(2):1-10(in Chinese)
    [12]
    Perc M. Evolution of cooperation on scale-free networks subject to error and attack. New Journal of Physics, 2009, 11:033027
    [13]
    Szolnoki A, Perc M, Danku Z. Towards effective payoffs in the Prisoner's Dilemma game on scale-free networks. Physica A, 2008, 387(8-9):2075-2082
    [14]
    Wang Z, Szolnoki A, Perc M. Evolution of public cooperation on interdependent networks:the impact of biased utility functions. EPL, 2012, 97(4):48001
    [15]
    Wang Z, Szolnoki A, Perc M. Interdependent network reciprocity in evolutionary games. Scientific Reports, 2013, 3:1183
    [16]
    Perc M, Gardeñes J G, Szolnoki A, Floria L M, Moreno Y. Evolutionary dynamics of group interactions on structured populations:a review. Journal of Royal Society Interface, 2013, 10(80):20120997
    [17]
    Szabó G, Tõke C. Evolutionary Prisoner's Dilemma game on a square lattice. Physical Review E, 1998, 58(1):69
    [18]
    Traulsen A, Nowak M A, Pacheco J M. Stochastic dynamics of invasion and fixation. Physical Review E, 2006, 74:011909
    [19]
    Cheng D Z, Qi H S, Li Z Q. Analysis and Control of Boolean Networks-A Semi-Tensor Product Approach. London:Springer, 2011
    [20]
    Cheng D Z, Qi H S, Zhao Y. An Introduction to Semi-Tensor Product of Matrices and Its Applications. Singapore:World Scientific, 2012
    [21]
    Gibbons R. A Primer in Game Theory. Glasgow:Bell and Bain Ltd., 1992
    [22]
    Xie Zheng. An Introduction to Game Theory. Beijing:Science Press, 2010(in Chinese)
    [23]
    Bazaraa M S, Sherali H D, Shetty C M. Nonlinear Programming-Theory and Algorithms (3rd edition). Hoboken:John Wiley and Sons, 2006
    [24]
    Pal R, Datta A, Dougherty E R. Optimal infinite-horizon control for probabilistic Boolean networks. IEEE Transactions on Signal Processing, 2006, 54(6):2375-2387

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