Tree Construction and Backward Induction: A Mobile Experiment

Abstract

Dynamic game theory has two fundamental goals: modeling how decision-makers perceive the interaction they participate in (tree construction) and identifying the strategies they select (backward induction). In our experiment, subjects often violate the theory (i.e., they do not construct a tree or backward induct), which is because either their skills are too low or the interaction is too complex. We use response times to measure skills and complexity. We find that complexity of interaction increases with its length and width; however, the length has a relatively bigger impact. Improving skills or decreasing complexity increases the likelihood of subjects behaving according to the theory; however, improving skills has a bigger impact. To collect the data, we developed a mobile application, Blues and Reds, comprising of 58 dynamic games. Our samples include 4,582 (analysis of tree construction) and 6,677 (analysis of backward induction) subjects coming from over 100 countries.

Keywords: game theory; mobile experiment; tree construction; backward induction