Xian-jia WANG
,
Rui DONG
,
Lin CHEN
. THE OPTIMAL CONTROL FOR PROMOTING THE COOPERATION IN EVOLUTION GAME GENERATED BY PRISONER'S DILEMMA[J]. Acta mathematica scientia, Series B, 2018
, 38(1)
: 73
-92
.
DOI: 10.1016/S0252-9602(17)30118-2
[1] Nowak M A. Evolving cooperation. J Theor Biol, 2012, 299:1-8
[2] Nowak M A. Five rules for the evolution of cooperation. Science, 2006, 314(5805):1560-1563
[3] Axelrod R, Hamiton W D. The evolution of cooperation. Science, 1981, 211(4489):1390-1396
[4] Li J. The effect of memory size on the evolutionary stability of strategies in iterated Prisoner's Dilemma. IEEE Tran Evol Comput, 2014, (186):819-826
[5] Nowak M A, Sigmund K. Evolution of indirect reciprocity. Nature, 2005, 437(7063):1291-1298
[6] Wedekind C, Milinski M. Cooperation through image scoring in humans. Science, 2000, 288(5467):850-852
[7] Nowak M A, Robert M M. Evolutionary games and spatial chaos. Nature, 1992, 359(6398):826-829
[8] Taylor P D, Day T, Wild G. Evolution of cooperation in a finite homogeneous graph. Nature, 2007, 447(7143):469-472
[9] Taylor C, Nowak M A. Transforming the dilemma. Evolution, 2007, 61(10):2281-2292
[10] Goodnight C J. Multilevel selection:the evolution of cooperation in non-kin groups. Popul Ecol, 2005, 471:3-12
[11] Lamba S. Social learning in cooperative dilemmas. Proc Roy Soc B:Biol Sci, 2014, 281(1787):4739-4753
[12] Benjamin A, Nowak M A. Games among relatives revisited. J Theor Biol, 2015, 378:103-116
[13] Vincent T L, Vincent, T L S. Evolution and control system design. IEEE Control Syst Mag, 2000, 20(5):20-35
[14] Cheng D Z, He F H, Qi H S. Modeling, analysis and control of networked evolutionary games. IEEE Trans Autom Control, 2015, 60(9):2402-2415
[15] Wang L, Wu T, Zhang Y L. Feedback mechanism in coevolutionary games. Control Theory & Applications, 2014, 31(7):823-836
[16] Liang H L, Cao M, Wang X F. Analysis and shifting, of stochastically stable equilibria for evolutionary snowdrift games. Systems & Control Letters, 2015, 85:16-22
[17] Sigmund K, De Silva H, Hauert C, Traulsen A. Social learning promotes institutions for governing the commons. Nature, 2010, 466:861-863
[18] Tatsuya S, Tatsuo U. Replicator dynamics in public goods games with reward funds. J Theor Biol, 2011, 287:109-114
[19] Liu Q L, Li X C. Effective stability control research of evolutionary game in China's coal mine safety supervision. J of Beijing Institute of Technology (Social Sciences Edition), 2015, 17(4):49-56
[20] Pan F, Xi B, Wang L. Analysis on environmental regulation strategy of local government based on evolutionary game theory. Syst Engi-Theo Prac, 2015, 35(6):1393-1404
[21] Tilman A R, Watson J R, Levin S. Maintaining cooperation in social-ecological systems. Theor Ecol, 2016:1-11
[22] Chiang A C. Fundamental Methods of Mathematical Economics. McGraw-Hill/Irwin, 2005
[23] Nuño G, Moll B. Controlling a Distribution of Heterogeneous Agents. Social Science Electronic Publishing, 2015
[24] Chaluba F A C C, and Souza M O. Discrete versus continuous models in evolutionary dynamics:from simple to simpler-and even simpler-models. Math Comput Model, 2006, 47(7):743-754
[25] Hofbauer J, Sigmund K. Evolutionary Games and Population Dynamics. Cambridge University Press, 1998
[26] Luo S. A unifying framework reveals key properties of multilevel selection. J Theor Biol, 2014, 341(2):41-52
[27] Wang X J, Lan J, Dong Q J, Lei G L. Evolutionary dynamics on one-dimensional cycle with shifting mechanism and tiny mutation rate. Acta Math Sci (English Series), 2015, 35(1):95-104
[28] Maynard-Smith J, Price G R. The logic of animal conflict. Nature, 1973, 246(5427):15-18