  An important issue in public goods game is whether player's behaviour changes
over time, and if so, how significant it is. In this game players can be
classified into different groups according to the level of their participation
in the public good. This problem can be considered as a concept drift problem
by asking the amount of change that happens to the clusters of players over a
sequence of game rounds. In this study we present a method for measuring
changes in clusters with the same items over discrete time points using
external clustering validation indices and area under the curve. External
clustering indices were originally used to measure the difference between
suggested clusters in terms of clustering algorithms and ground truth labels
for items provided by experts. Instead of different cluster label comparison,
we use these indices to compare between clusters of any two consecutive time
points or between the first time point and the remaining time points to measure
the difference between clusters through time points. In theory, any external
clustering indices can be used to measure changes for any traditional
(non-temporal) clustering algorithm, due to the fact that any time point alone
is not carrying any temporal information. 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.
