An Empirical Measure of Tree Complexity

Game-theoretic trees vary in complexity. To rank trees by their complexity, this paper relies on the subjects’ behavior to define and derive the empirical measure of tree complexity. Data comes from the mobile app Blues and Reds, designed specifically to conduct experiments. The sample consists of 6,637 subjects from 143 countries who play 27 different dynamic games. Based on subjects’ response times, we find that two measures – the average response time spent at the first round and the average total time spent solving the tree – are the best candidates for the empirical measure of tree complexity.