Game-theoretic trees vary in complexity. This paper, “Measuring Tree Complexity With Response Times,” introduced the concept of graph-based complexity and relied on the subjects’ behavior to empirically derive a measure of tree complexity. Data came from the mobile app Blues and Reds, designed specifically to conduct experiments.

The sample consisted of 6637 subjects from 143 countries who played 27 different dynamic games. Based on subjects’ response times, the authors found that two measures—the average response time spent at the first round and the average total time spent solving the tree—were the best candidates for the empirical measure of tree complexity. They focused on two-person, finite, zero-sum dynamic games with perfect and complete information.

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Konrad Grabiszewski, Alex Horenstein, Measuring tree complexity with response times, Journal of Behavioral and Experimental Economics, Volume 98, 2022, 101876, ISSN 2214-8043, https://doi.org/10.1016/j.socec.2022.101876.