Measuring Behavioural Change of Players in Public Goods Game

  • Polla Fattah
  • Uwe Aickelin
  • Christian Wagner
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 751)


In the public goods game, players can be classified into different types according to their participation in the game. It is an important issue for economists to be able to measure players’ strategy changes over time which can be considered as concept drift. In this study, we present a method for measuring changes in items’ cluster membership in temporal data. The method consists of three steps in the first step, the temporal data will be transformed into a discrete series of time points then each time point will be clustered separately. In the last step, the items’ membership in the clusters is compared with a reference of behaviour to determine the amount of behavioural change in each time point. Different external cluster validity indices and area under the curve are used to measure these changes. Instead of different cluster label comparison, we use these indices a new way to compare between clusters and reference points. In this study, three categories of reference of behaviours are used 1- first time point, 2- previous time pint and 3- the general overall behaviour of the items. For the public goods game, our results indicate that the players are changing over time but the change is smooth and relatively constant between any two time points.



The authors record their thanks to Simon Gaechter and Felix Kolle in the School of Economics at the University of Nottingham for providing us with data from the public goods experiment and taking time to explain it to us.


  1. 1.
    Aggarwal, C.C.: On change diagnosis in evolving data streams. IEEE Trans. Knowl. Data Eng. 17(5), 587–600 (2005)CrossRefGoogle Scholar
  2. 2.
    Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Pé rez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recogn. 46, 243–256 (2012)CrossRefGoogle Scholar
  3. 3.
    Baena-Garcia, M., del Campo-Avila, J., Fidalgo, R., Bifet, A., Gavalda, R., Morales-Bueno, R.: Early drift detection method. In: 4th ECML PKDD International Workshop on Knowledge Discovery from Data Streams, pp. 77–86 (2006)Google Scholar
  4. 4.
    Böttcher, M., Höppner, F., Spiliopoulou, M.: On exploiting the power of time in data mining. ACM SIGKDD Explor. Newsl. 10(2), 3–11 (2008). DecCrossRefGoogle Scholar
  5. 5.
    Bradley, A.P.: The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recogn. 30(7), 1145–1159 (1997)CrossRefGoogle Scholar
  6. 6.
    Elwell, R., Polikar, R.: Incremental learning of concept drift in nonstationary environments. IEEE Trans. Neural Netw. 22(10), 1517–1531 (2011)CrossRefGoogle Scholar
  7. 7.
    Fattah, P., Aickelin, U., Wagner, C.: Optimising rule-based classification in temporal data. Zanco J. Pure Appl. Sci. 28(2), 135–146 (2016)Google Scholar
  8. 8.
    Figuières, C., Masclet, D., Willinger, M.: Weak moral motivation leads to the decline of voluntary contributions. J. Public Econ. Theory 15(5), 745–772 (2013)CrossRefGoogle Scholar
  9. 9.
    Fischbacher, U., Gächter, S.: Social preferences, beliefs, and the dynamics of free riding in public goods experiments. Am. Econ. Rev. 100(1), 541–556 (2010)CrossRefGoogle Scholar
  10. 10.
    Fischbacher, U., Gachter, S., Quercia, S., Gächter, S.: The behavioral validity of the strategy method in public good experiments. J. Econ. Psychol. 33(4), 897–913 (2012). AugCrossRefGoogle Scholar
  11. 11.
    Fischbacher, U., Gächter, S., Whitehead, K.: Heterogeneous social preferences and the dynamics of free riding in public good experiments about the centre or contact. Am. Econ. Rev. 100(1), 541–556 (2010)CrossRefGoogle Scholar
  12. 12.
    Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc. 78(383), 553–569 (1983)Google Scholar
  13. 13.
    Gama, J., Zliobaite, I., Bifet, A., Pechenizkiy, M., Bouchachia, Abdelhamid: A survey on concept drift adaptation. ACM Comput. Surv. (CSUR) 46(4), 44 (2014)CrossRefzbMATHGoogle Scholar
  14. 14.
    Garnett, Roman., Roberts, S.J.: Learning from Data Streams with Concept Drift. Technical Report PARG-08-01, Department of Engineering Science, University of Oxford (2008)Google Scholar
  15. 15.
    Günnemann, S., Kremer, H., Laufkotter, C., Seidl, T.: Tracing evolving clusters by subspace and value similarity. Adv. Knowl. Discov. Data Min. 6635, 444–456 (2011)Google Scholar
  16. 16.
    Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Cluster validity methods: part I. ACM Sigmod Rec. 31(2), 40–45 (2002)CrossRefGoogle Scholar
  17. 17.
    Harel, M., Mannor, S., El-Yaniv, R., Crammer, K.: Concept drift detection through resampling. In: Proceedings of the 31st International Conference on Machine Learning (ICML-14), pp. 1009–1017 (2014)Google Scholar
  18. 18.
    Hawwash, B., Nasraoui, O.O.: Stream-dashboard: a framework for mining, tracking and validating clusters in a data stream. In: Proceedings of the 1st International Workshop on Big Data, Streams and Heterogeneous Source Mining: Algorithms, Systems, Programming Models and Applications, pp. 109–117 (2012)Google Scholar
  19. 19.
    Jain, A.K.: Data clustering: 50 years beyond K-means. Pattern Recogn. Lett. 31, 651–666 (2010)CrossRefGoogle Scholar
  20. 20.
    Kalnis, P., Mamoulis, N., Bakiras, S.: On discovering moving clusters in spatio-temporal data. Adv. Spat. Temporal Databases 3633, 364–381 (2005)CrossRefGoogle Scholar
  21. 21.
    Kaul, I., Grungberg, I., Stern, M.A.: Global public goods. In: Global Public Goods (1999)Google Scholar
  22. 22.
    Keser, C., van Winden, F.: Conditional cooperation and voluntary contributions to public goods. Scand. J. Econ. 102, 23–39 (2000)CrossRefGoogle Scholar
  23. 23.
    Meil, M.: Comparing clusterings an information based distance. J. Multivar. Anal. 98(5), 873–895 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Meila, M.: Comparing clusterings by the variation of information. In: Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, Washington, DC, USA, 24–27 Aug 2003, proceedings, p. 173 (2003)Google Scholar
  25. 25.
    Ntoutsi, I., Spiliopoulou, M., Theodoridis, Y.: Tracing cluster transitions for different cluster types. Control Cybern. 38(1), 239–259 (2009)zbMATHGoogle Scholar
  26. 26.
    Ntoutsi, I., Spiliopoulou, M., Theodoridis, Y.: Summarizing cluster evolution in dynamic environments. In: Computational Science and Its Applications—ICCSA 2011, vol. 6783, pp. 562–577. Springer, Berlin, Heidelberg (2011)Google Scholar
  27. 27.
    Rendón, E., Abundez, I.: Internal versus external cluster validation indexes. Int. J. Comput. Commun. 5(1), 27–34 (2011)Google Scholar
  28. 28.
    Rezaei, M., Franti, P.: Set matching measures for external cluster validity. IEEE Trans. Knowl. Data Eng. 28(8), 2173–2186 (2016)CrossRefGoogle Scholar
  29. 29.
    Spiliopoulou, M., Ntoutsi, E., Theodoridis, Y., Schult, R.: MONIC and followups on modeling and monitoring cluster transitions. Mach. Learn. Knowl. Discov. Databases 8190(2013), 622–626 (2013)CrossRefGoogle Scholar
  30. 30.
    Spiliopoulou, M., Ntoutsi, I., Theodoridis, Y., Schult, R.: Monic: modeling and monitoring cluster transitions. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 706–711 (2006)Google Scholar
  31. 31.
    Tsymbal, A.: The problem of concept drift: definitions and related work. Computer Science Department, Trinity College Dublin (2004)Google Scholar
  32. 32.
    Vendramin, L., Campello, R.J.G.B., Hruschka, E.R.: Relative clustering validity criteria: a comparative overview. Stat. Anal. Data Min. 4(3), 209–235 (2010)Google Scholar
  33. 33.
    Xiaofeng, L., Weiwei, G.: Study on a classification model of data stream based on concept drift. Int. J. Multimedia Ubiquitous Eng. 9(5), 363–372 (2014)CrossRefGoogle Scholar
  34. 34.
    Yang, D., Guo, Z., Rundensteiner, E.A., Ward, M.O.: CLUES: a unified framework supporting interactive exploration of density-based clusters in streams. In: Proceedings of the 20th ACM International Conference on Information and Knowledge Management, pp. 815–824 (2011)Google Scholar
  35. 35.
    Zaki, M.J., Meira Jr., M.: Data Mining and Analysis: Fundamental Concepts and Algorithms. Cambridge University Press, New York (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.School of Computer ScienceThe University of NottinghamNottinghamUK
  2. 2.School of Computer ScienceThe University of Nottingham NingboNingboChina

Personalised recommendations