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Strategy Selection in Evolutionary Game Dynamics on Group Interaction Networks

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Abstract

Evolutionary game theory provides an appropriate tool for investigating the competition and diffusion of behavioral traits in biological or social populations. A core challenge in evolutionary game theory is the strategy selection problem: Given two strategies, which one is favored by the population? Recent studies suggest that the answer depends not only on the payoff functions of strategies but also on the interaction structure of the population. Group interactions are one of the fundamental interactive modes within populations. This work aims to investigate the strategy selection problem in evolutionary game dynamics on group interaction networks. In detail, the strategy selection conditions are obtained for some typical networks with group interactions. Furthermore, the obtained conditions are applied to investigate selection between cooperation and defection in populations. The conditions for evolution of cooperation are derived for both the public goods game and volunteer’s dilemma game. Numerical experiments validate the above analytical results.

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References

  • Antal T, Scheuring I (2006) Fixation of strategies for an evolutionary game in finite populations. Bull Math Biol 68:1923–1944

    Article  MathSciNet  MATH  Google Scholar 

  • Antal T, Nowak MA, Traulsen A (2009) Strategy abundance in \(2\times 2\) games for arbitrary mutation rates. J Theor Biol 257:340–344

    Article  MathSciNet  Google Scholar 

  • Antal T, Traulsen A, Ohtsuki H, Tarnita CE, Nowak MA (2009) Mutation–selection equilibrium in games with multiple strategies. J Theor Biol 258:614–622

    Article  MathSciNet  Google Scholar 

  • Axelrod R, Hamilton WD (1981) The evolution of cooperation. Science 211:1390–1396

    Article  MathSciNet  MATH  Google Scholar 

  • Bentley RA, Hahn MW, Shennan SJ (2004) Random drift and culture change. Proc R Soc B 271(1547):1443–1450

    Article  Google Scholar 

  • Brandt H, Hauert C, Sigmund K (2003) Punishment and reputation in spatial public goods games. Proc R Soc B 270:1099–1104

    Article  Google Scholar 

  • Broom M, Rychtář J (2009) An analysis of the fixation probability of a mutant on special class of non-directed graphs. Proc R Soc A 464:2609–2627

    Article  Google Scholar 

  • Chuang JS, Rivoire O, Leibler S (2009) Simpsons paradox in a synthetic microbial system. Science 323:272–275

    Article  Google Scholar 

  • Cremer J, Melbinger A, Frey E (2012) Growth dynamics and the evolution of cooperation in microbial populations. Sci Rep 2. doi:10.1038/srep00281

  • Doebeli M, Knowlto N (1998) The evolution of interspecific mutualisms. Proc Natl Acad Sci USA 95:8676–8680

    Article  Google Scholar 

  • Ewens WJ (ed) (2004) Mathematical population genetics, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Fu F, Tarnita CE, Christakis NA, Wang L, Rand DG, Nowak MA (2012) Evolution of in-group favoritism. Sci Rep 2 . doi:10.1038/srep00460

  • Gokhale CS, Traulsen A (2010) Evolutionary games in the multiverse. Proc Natl Acad Sci USA 107:5500–5504

    Article  Google Scholar 

  • Griffin AS, West SA, Buckling A (2004) Cooperation and competition in pathogenic bacteria. Nature 430:1024–1027

    Article  Google Scholar 

  • Herzog HA, Bentley RA, Hahn MW (2004) Random drift and large shifts in popularity of dog breeds. Proc R Soc B 271(Suppl. 5):353–356

    Article  Google Scholar 

  • Johnson DDP, Stopka P, Knights S (2003) Sociology: the puzzle of human cooperation. Nature 421:911–912

    Article  Google Scholar 

  • Langer P, Nowak MA, Hauert C (2008) Spatial invasion of cooperation. J Theor Biol 250:634–641

    Article  MathSciNet  Google Scholar 

  • Lawler GF (ed) (2006) Introduction to stochastic processes, 2nd edn. Chapman and Hall, New York

    MATH  Google Scholar 

  • Lieberman E, Hauert C, Nowak MA (2005) Evolutionary dynamics on graphs. Nature 433:312–316

    Article  Google Scholar 

  • Nowak MA (2006) Evolutionary dynamics: exploring the equation of life. Harvard University Press, Cambridge

    Google Scholar 

  • Nowak MA (2006) Five rules for the evolution of cooperation. Science 314:1560–1563

    Article  Google Scholar 

  • Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359:826–829

    Article  Google Scholar 

  • Nowak MA, Sigmund K (2005) Evolution of indirect reciprocity. Nature 427:1291–1298

    Article  Google Scholar 

  • Nowak MA, Tarnita CE, Antal T (2010) Evolutionary dynamics in structured populations. Philos Trans R Soc B 365:19–30

    Article  Google Scholar 

  • Ohtsuki H (2010) Stochastic evolutionary dynamics of bimatrix games. J Theor Biol 264:136–142

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Ohtsuki H, Nowak MA (2006) Evolutionary games on cycles. Proc R Soc B 273:2249–2256

    Article  Google Scholar 

  • Perc M, Gomez-Gardenes J, Szolnoki A, Floria LM, Moreno Y (2013) Evolutionary dynamics of group interactions on structured populations: a review. J R Soc Interface 10. doi:10.1098/rsif.2012.0997

  • Rainey PB, Rainey K (2003) Evolution of cooperation and conflict in experimental bacterial populations. Nature 425:72–74

    Article  Google Scholar 

  • Samuelson L (1997) Evolutionary games and equilibrium selection. MIT Press, Cambridge

    MATH  Google Scholar 

  • Santos FC, Pacheco JM, Lenaerts T (2006) Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc Natl Acad Sci USA 103:3490–3494

    Article  Google Scholar 

  • Santos FC, Santos MD, Pacheco JM (2008) Social diversity promotes the emergence of cooperation in public goods games. Nature 454:213–216

    Article  Google Scholar 

  • Smith JM (1982) Evolution and the theory of games. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Smith JM, Price GR (1973) The logic of animal conflict. Nature 246:15–18

    Article  Google Scholar 

  • Szabó G, Fath G (2007) Evolutionary games on graphs. Phys Rep 446:97–216

    Article  MathSciNet  Google Scholar 

  • Szolnoki A, Perc M, Szabó G (2009) Topology-independent impact of noise on cooperation in spatial public goods games. Phys Rev E 80. doi:10.1103/PhysRevE.80.056109

  • Tan S, Lu J (2014) Characterizing the effect of population heterogeneity on evolutionary dynamics on complex networks. Sci Rep 4. doi:10.1038/srep05034

  • Tan S, Lu J, Yu X, Hill D (2013) Evolution and maintenance of cooperation via inheritance of neighborhood relationship. Chin Sci Bull 58:3491–3498

    Article  Google Scholar 

  • Tan S, Lu J, Chen G, Hill D (2014a) When structure meets function in evolutionary dynamics on complex networks. IEEE Circ Syst Mag (in press)

  • Tan S, Lu J, Hill D (2014b) Towards a theoretical framework for analysis and intervention of random drift on general networks. IEEE Trans Autom Contr. doi:10.1109/TAC.2014.2329235

  • Tang C, Li X, Cao L, Zhan J (2012) The \(\sigma \) lar of evolutionary dynamics in community-structured population. J Theor Biol 306:1–6

    Article  MathSciNet  Google Scholar 

  • Tarnita CE, Antal T, Ohtsuki H, Nowak MA (2009) Evolutionary dynamics in set structured populations. Proc Natl Acad Sci 106:8601–8604

    Article  Google Scholar 

  • Tarnita CE, Ohtsuki H, Antal T, Fu F, Nowak MA (2009) Strategy selection in structured populations. J Theor Biol 259:570–581

    Article  MathSciNet  Google Scholar 

  • Tarnita CE, Wage N, Nowak MA (2011) Multiple strategies in structured populations. Proc Natl Acad Sci USA 108:2334–2337

    Article  Google Scholar 

  • Velicer GJ, Yu YN (2003) Evolution of novel cooperative swarming in the bacterium Myxococcus xanthus. Nature 425:75–78

    Article  Google Scholar 

  • Wu B, Zhou D, Fu F, Luo Q, Wang L (2010) Evolution of cooperation on stochastic dynamical networks. PloS ONE 5. doi:10.1371/journal.pone.0011187

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Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China under Grants 61304151 and Grants 61304157, and the Science Foundation of Henan University under Grants 2012YBZR007.

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Hunan University, Changsha, 410082, China

    Shaolin Tan

  2. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Shaolin Tan & Shasha Feng

  3. Beijing National Day School, Beijing, 100039, China

    Shasha Feng

  4. School of Mathematics and Information Sciences, Henan University, Kaifeng, 475004, China

    Pei Wang

  5. School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Yao Chen

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  1. Shaolin Tan
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  2. Shasha Feng
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  4. Yao Chen
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Correspondence to Shaolin Tan.

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Tan, S., Feng, S., Wang, P. et al. Strategy Selection in Evolutionary Game Dynamics on Group Interaction Networks. Bull Math Biol 76, 2785–2805 (2014). https://doi.org/10.1007/s11538-014-0031-y

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  • DOI: https://doi.org/10.1007/s11538-014-0031-y

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