A Mobile Experiment on Tree Construction

Abstract

A game-theoretic tree is a formidable way of representing dynamic interactions. However, no real-life interaction comes with its own tree representation. Before deciding on what strategy to choose, decision-makers must understand the interaction they are participating in. In the language of game theory, they construct a tree. Together with backward induction, tree construction constitutes the foundations of dynamic game theory. This article asks whether people correctly construct trees. Since how people understand the reality is unobservable, the main challenge is to design a test that studies subjects' unobservable perception through their observable choices. The proposed test consists of two steps: first, screening for backward-inducting subjects and second, testing them for tree construction. Replicated in 27 different interactions with 5,001 subjects from 133 countries, the test shows that between 13% and 63% of backward-inducting subjects fail at tree construction. This result is detrimental for the internal validity of testing backward induction. In order to collect the data, a team of professional developers was hired to create Blues and Reds, a mobile app that functions as an experiment and has been available for free on iOS and Android since August 2017.

Keywords: dynamic games, tree construction, perception, backward induction, experimental game theory, mobile experiment

JEL Classification: C72, C99, D91