An Empirical Measure of Tree Complexity

19 Pages Posted: 15 Oct 2019

See all articles by Konrad Grabiszewski

Konrad Grabiszewski

Mohammad bin Salman College

Alex R. Horenstein

University of Miami - School of Business Administration - Department of Economics

Date Written: October 3, 2019

Abstract

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

Suggested Citation

Grabiszewski, Konrad and Horenstein, Alex R., An Empirical Measure of Tree Complexity (October 3, 2019). Available at SSRN: https://ssrn.com/abstract=3463988 or http://dx.doi.org/10.2139/ssrn.3463988

Konrad Grabiszewski

Mohammad bin Salman College ( email )

KAEC
Saudi Arabia

Alex R. Horenstein (Contact Author)

University of Miami - School of Business Administration - Department of Economics ( email )

P.O. Box 248126
Coral Gables, FL 33124-6550
United States

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