Finite Population Trust Game Replicators

  • Garrison Greenwood
  • Hussein AbbassEmail author
  • Eleni Petraki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9592)


Our previous work introduced the N player trust game and examined the dynamics of this game using replicator dynamics for an infinite population. In finite populations, quantization becomes a necessity that introduces discontinuity in the trajectory space, which can impact the dynamics of the game differently. In this paper, we present an analysis of replicator dynamics of the N player trust game in finite populations. The analysis reveals that, quantization indeed introduces fixed points in the interior of the 2-simplex that were not present in the infinite population analysis. However, there is no guarantee that these fixed points will continue to exist for any arbitrary population size; thus, they are clearly an artifact of quantization. In general, the evolutionary dynamics of the finite population are qualitatively similar to the infinite population. This suggests that for the proposed trust game, trusters will be extinct if the population contains an untrustworthy player. Therefore, trusting is an evolutionary unstable strategy.


Trust Evolutionary game theory N-person trust game 


  1. 1.
    Abbass, H., Greenwood, G., Petraki, E.: The \(n\)-player trust game and its replicator dynamics. IEEE Trans. Evol. Comput. (to appear). doi: 10.1109/TEVC.2015.2484840
  2. 2.
    Chandrasekhar, V., Reznik, Y., Takacs, G., Chen, D., Tsai, S., Grzeszczuk, R., Girod, R.: Quantization schemes for low bitrate compressed histogram of gradients descriptors. In: 2010 IEEE Computer Vision and Pattern Recognition Workshops, pp. 33–40 (2010)Google Scholar
  3. 3.
    David, O.E., van den Herik, H.J., Koppel, M., Netanyahu, N.S.: Genetic algorithms for evolving computer chess programs. IEEE Trans. Evol. Comput. 18(5), 779–789 (2014)CrossRefzbMATHGoogle Scholar
  4. 4.
    Ficici, S., Pollack, J.: Effects of finite populations on evolutionary stable strategies. In: GECCO, pp. 927–933 (2000)Google Scholar
  5. 5.
    Fogel, D., Fogel, G., Andrews, P.: On the instability of evolutionary stable strategies. BioSystems 44, 135–152 (1997)CrossRefGoogle Scholar
  6. 6.
    Fogel, G., Andrews, P., Fogel, D.: On the instability of evolutionary stable strategies in small populations. Ecol. Model. 109, 283–294 (1998)CrossRefGoogle Scholar
  7. 7.
    Greenwood, G.W.: Emotions and their effect on cooperation levels in n-player social dilemma games. In: Chalup, S.K., Blair, A.D., Randall, M. (eds.) ACALCI 2015. LNCS, vol. 8955, pp. 88–99. Springer, Heidelberg (2015) Google Scholar
  8. 8.
    Hofbauer, J., Sigmund, K.: Evolutionary game dynamics. Bull. Am. Math. Soc. 40(4), 479–519 (2003)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Li, J., Kendall, G.: The effect of memory size on the evolutionary stability of strategies in iterated prisoner’s dilemma. IEEE Trans. Evol. Comput. 18(6), 819–826 (2014)CrossRefGoogle Scholar
  10. 10.
    Moran, P.A.P.: The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford (1962)zbMATHGoogle Scholar
  11. 11.
    Nowak, M.: Five rules for the evolution of cooperation. Science 314(5805), 1560–1563 (2006)CrossRefGoogle Scholar
  12. 12.
    Petraki, E., Abbass, H.A.: On trust and influence: a computational red teaming game theoretic perspective. In: 2014 Seventh IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA), pp. 1–7 (2014)Google Scholar
  13. 13.
    Putnam, R.D.: Comunidade e democracia: a experiência da Itália moderna. FGV Editora (2000)Google Scholar
  14. 14.
    Shmueli, E., Singh, V.K., Lepri, B., Pentland, A.: Sensing, understanding, and shaping social behavior. IEEE Trans. Comput. Soc. Syst. 1(1), 22–34 (2014)CrossRefGoogle Scholar
  15. 15.
    Yeh, C., Yang, C.: Social networks and asset price dynamics. IEEE Trans. Evol. Comput. 19(3), 387–399 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Garrison Greenwood
    • 1
  • Hussein Abbass
    • 2
    Email author
  • Eleni Petraki
    • 3
  1. 1.Electrical and Computer Engineering DepartmentPortland State UniversityPortlandUSA
  2. 2.School of Engineering and Information TechnologyUniversity of New South WalesCanberraAustralia
  3. 3.Faculty of Arts and DesignUniversity of CanberraCanberraAustralia

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