Abstract
Networked evolutionary games provide an appropriate tool for investigating competition and diffusion of behavioral traits in structured biological and social populations. A core challenge in networked evolutionary game theory is the strategy selection problem: Given several strategies, which one is favored by the population? This chapter is to explore and analyze the strategy selection problem in several typical evolutionary dynamic models of networked games. In detail, firstly the concept of networked games is introduced together with several typical evolutionary dynamics models, including the birth-death process, the death-birth process, and the imitation dynamics. Then, several results of strategy selection conditions are reported for evolutionary dynamics of both two-player multi-strategy games and multi-player two-strategy games on networks. Moreover, these results are applied to the prisoner’s dilemma game, the volunteer’s dilemma game, and the public goods game to investigate the cooperation conditions in networked populations. The main aim of this chapter is to characterize the effect of interacting networks on strategy selection and more specifically on the evolution of cooperation.
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References
Smith, J.M.: Evolution and The Theory of Games. Cambridge University Press, Cambridge (1982)
Nowak, M.A.: Evolutionary Dynamics: Exploring the Equation of Life. Harvard University Press, Cambridge (2006)
Camerer, C.: Behavioral Game Theory. Princeton University Press, Princeton (2003)
Smith, J.M., Price, G.R.: The logic of animal conflict. Nature 246, 15–18 (1973)
Axelrod, R., Hamilton, W.D.: The evolution of cooperation. Science 211, 1390–1396 (1981)
Doebeli, M., Knowlto, N.: The evolution of interspecific mutualisms. Proc. Natl. Acad. Sci. USA 95, 8676–8680 (1998)
Samuelson, L.: Evolutionary Games and Equilibrium Selection. MIT Press, Cambridge (1997)
Szabó, G., Fath, G.: Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)
Weibull, J.W.: Evolutionary game theory. The MIT Press, Cambridge (1995)
Ohtsuki, H.: Stochastic evolutionary dynamics of bimatrix games. J. Theor. Biol. 264, 136–142 (2010)
Hofbauer, J., Sigmund, K.: Evolutionary games and population dynamics. Cambridge University Press, Cambridge (1998)
Nowak, M.A., Sigmund, K.: Evolutionary dynamics of biological games. Science 303, 793–799 (2004)
Bentley, R.A., Hahn, M.W., Shennan, S.J.: Random drift and culture change. Proc. R. Soc. B 271, 1443–1450 (2004)
Herzog, H.A., Bentley, R.A., Hahn, M.W.: Random drift and large shifts in popularity of dog breeds. Proc. R. Soc. B 271, 353–356 (2004)
Ziman, J. (ed.): Technological Innovation as An Evolutionary Process. Cambridge University Press, Cambridge (2000)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)
Lu, J., Leung, H., Chen, G.: Complex dynamical networks: modeling, synchronization and control. Dyn. continuous. Discret. Ser. B 11a, 70–77 (2004)
Lu, J., Chen, G.: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Autom. Control. 50, 841–846 (2005)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)
Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Newman, M.E.J., Watts, D.J.: Renormalization group analysis of the small-world network model. Phys. Lett. A 263, 341–346 (1999)
Nowak, M.A., Tarnita, C.E., Antal, T.: Evolutionary dynamics in structured populations. Philos. Trans. R. Soc. B 365, 19–30 (2010)
Velicer, G.J., Yu, Y.N.: Evolution of novel cooperative swarming in the bacterium Myxococcus xanthus. Nature 425, 75–78 (2003)
Perc, M., Gomez-Gardenes, J., Szolnoki, A., Floria, L.M., Moreno, Y.: Evolutionary dynamics of group interactions on structured populations: a review. J. R. Soc. Interface 10, 20120997 (2013)
Ewens, W.J.(ed.): Mathematical Population Genetics. 2nd edn. Springer, New York (2004)
Tan, S., Lu, J., Chen, G., Hill, D.: When structure meets functions in evolutionary dynamics on complex networks. IEEE Circuits Syst. Mag. 14, 36–50 (2014)
Wu, B., Zhou, D., Fu, F., Luo, Q., Wang, L.: Evolution of cooperation on stochastic dynamical networks. PLoS ONE 5, e11187 (2010)
Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)
Johnson, D.D.P., Stopka, P., Knights, S.: Sociology-the puzzle of human cooperation. Nature 421, 911–912 (2003)
Langer, P., Nowak, M.A., Hauert, C.: Spatial invasion of cooperation. J. Theor. Biol. 250, 634–641 (2008)
Tan, S., Lu, J., Yu, X., Hill, D.: Evolution and maintenance of cooperation via inheritance of neighborhood relationship. Chin. Sci. Bull. 58, 3491–3498 (2013)
Ohtsuki, H., Nowak, M.A.: Evolutionary games on cycles. Proc. R. Soc. B 273, 2249–2256 (2006)
Tarnita, C.E., Ohtsuki, H., Antal, T., Fu, F., Nowak, M.A.: Strategy selection in structured populations. J. Theor. Biol. 259, 570–581 (2009)
Tarnita, C.E., Antal, T., Ohtsuki, H., Nowak, M.A.: Evolutionary dynamics in set structured populations. Proc. Natl. Acad. Sci. 106, 8601–8604 (2009)
Tang, C., Li, X., Cao, L., Zhan, J.: The \(\sigma \) lar of evolutionary dynamics in community-structured population. J. Theor. Biol 306, 1–6 (2012)
Tan, S., Feng, S., Wang, P., Chen, Y.: Strategy selection in evolutionary game dynamics on group interaction networks. Bull. Math. Biol. 76, 2785–2805 (2014)
Rainey, P.B., Rainey, K.: Evolution of cooperation and conflict in experimental bacterial populations. Nature 425, 72–74 (2003)
Griffin, A.S., West, S.A., Buckling, A.: Cooperation and competition in pathogenic bacteria. Nature 430, 1024–1027 (2004)
Nowak, M.A., Sigmund, K.: Evolution of indirect reciprocity. Nature 427, 1291–1298 (2005)
Nowak, M.A.: Five rules for the evolution of cooperation. Science 314, 1560–1563 (2006)
Santos, F.C., Pacheco, J.M., Lenaerts, T.: Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl. Acad. Sci. USA 103, 3490–3494 (2006)
Cremer, J., Melbinger, A., Frey, E.: Growth dynamics and the evolution of cooperation in microbial populations. Sci. Rep. 2, 281 (2012)
Santos, F.C., Santos, M.D., Pacheco, J.M.: Social diversity promotes the emergence of cooperation in public goods games. Nature 454, 213–216 (2008)
Brandt, F., Fischer, F., Holzer, M.: Equilibria of graphical games with symmetries. Theor. Comput. Sci. 31, 675–685 (2011)
Gokhale, C.S., Traulsen, A.: Evolutionary games in the multiverse. Proc. Natl. Acad. Sci. USA 107, 5500–5504 (2010)
Tan, S., Lu, J., Hill, D.: Towards a theoretical framework for controlling random drift on complex networks. IEEE Trans. Autom. Control 60, 576–582 (2015)
Tan, S., Lu, J.: Characterizing the effect of population heterogeneity on evolutionary dynamics on complex networks. Sci. Rep. 4, 5034 (2014)
Broom, M., Rychtář, J.: An analysis of the fixation probability of a mutant on special class of non-directed graphs. Proc. R. Soc. A 464, 2609–2627 (2009)
Lieberman, E., Hauert, C., Nowak, M.A.: Evolutionary dynamics on graphs. Nature 433, 312–316 (2005)
Tan, S., Lu, J., Hu, Y., Ogorzalek, M.J.: Explore strategy selection in populations via a continuous networked game dynamics. In: Proceeding IEEE International Symposium Circuits System, Melbourne, Australia, June 1–5 (2014)
Nowak, M.A., Sasaki, A., Taylor, C., Fudenberg, D.: Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)
Taylor, C., Fudenberg, D., Sasaki, A., Nowak, M.A.: Evolutionary game dynamics in finite populations. Bull. Math. Biol. 66, 1621–1644 (2004)
Ohtsuki, H., Hauert, C., Lieberman, E., Nowak, M.A.: A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)
Konno, T.: A condition for cooperation in a game on complex networks. J. Theor. Biol. 269, 224–233 (2011)
Antal, T., Traulsen, A., Ohtsuki, H., Tarnita, C.E., Nowak, M.A.: Mutation-selection equilibrium in games with multiple strategies. J. Theor. Biol. 258, 614–622 (2009)
Tarnita, C.E., Wage, N., Nowak, M.A.: Multiple strategies in structured populations. Proc. Natl. Acad. Sci. USA 108, 2334–2337 (2011)
Acknowledgments
This work was supported the 973 Project under Grant 2014CB845302, the Fundamental Research Funds for the Central Universities, the National Science and Technology Major Project of China under Grant 2014ZX10004-001-014, and the National Natural Science Foundation of China under Grant 61025017.
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Tan, S., Lü, J. (2016). Strategy Selection in Networked Evolutionary Games: Structural Effect and the Evolution of Cooperation. In: Lü, J., Yu, X., Chen, G., Yu, W. (eds) Complex Systems and Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47824-0_17
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DOI: https://doi.org/10.1007/978-3-662-47824-0_17
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