An Empirical Measure of Tree Complexity
19 Pages Posted: 15 Oct 2019
Date Written: October 3, 2019
Game-theoretic trees vary in complexity. To rank trees by their complexity, we rely 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 various dynamic games. Based on subjects' response times, we find that both 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. The derived measure serves the role of a control variable in empirical studies where controlling for complexity is required. With this new measure of complexity, we are able to observe that higher complexity implies a lower probability of subjects backward inducting. This result adds tree complexity as a new explanation of violations of backward induction.
Keywords: tree, complexity, backward induction, experimental game theory, mobile experiment
JEL Classification: C72, C73, C80, C90
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