Measuring Player's Behaviour Change over Time in Public Goods Game

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.