Doctoral Dissertation Research in Economics: Two Experiments on the Behavioral Equivalence of Dirty Faces Games

California Institute Of Technology, Pasadena CA

Investigators

Abstract

One of the main goals of behavioral economics is to better understand the implications of human cognitive limitations on behavior in strategic settings related to economic, social, and political competition. This branch of behavioral economics, behavioral game theory, focuses on how people form expectations in strategic environments about the anticipated behavior of other individuals. This project will experimentally investigate the “dirty faces game”, a workhorse example of a strategic environment where individuals can observe some actions by other players in the game that enable them to make inferences leading to more informed decisions. This is a simple but illustrative game that models situations where people update their beliefs and make decisions based on others’ past behavior, such as choosing a restaurant or purchasing a new product by reading reviews by other people. Classical theory about behavior in games, based on assumptions of perfect rationality, makes behaviorally implausible predictions in this game. Relaxing the assumption of perfect rationality leads to drastically different predictions about behavior in the dirty faces game, which makes it an ideal test bed for a new “dynamic cognitive hierarchy theory” (DCH) that predicts that, in dirty faces games, players will generally behave differently under two different conventional experimental protocols (direct response vs. strategy method), while the standard theory does not predict any behavioral difference. This project designs two experiments to detect the behavioral differences predicted by DCH in these games. A long-run goal of this project is not only to test the theory, but also to provide insights to policy designs that take account of cognitive limitations. Armed with improved theoretical models, policy makers can design more cognitively robust auctions, tax schemes, regulations, and other mechanisms to improve economic performance. The dirty faces game is a strategic environment where each individual within a group of individuals has either a dirty or a clean face and can see all other players’ faces but not their own faces. Over a sequence of decision periods, each individual can take an action that provides some information about the faces they see, and the ultimate goal of each individual is to learn their own face type from observing the others’ actions. At the beginning of the game, an honest announcement is made by an observer about whether or not there is at least one dirty face. From the standard game-theoretic perspective, players will eventually learn whether their face is dirty or clean. Moreover, the extensive and strategic form representations of this game are strategically equivalent and make the same classical predictions. However, from the psychological perspective, the mental processes are completely different---in the strategic form representation, players make inferences based on hypothetical events while in the extensive form representation, players can make statistical inferences based on observed behavior. In a two-person dirty faces game, equilibrium theory predicts players will know their face type within two periods---regardless of the payoffs and the representations (extensive form vs. strategic form). Specifically, DCH predicts both the payoff structure and game-form representation will jointly affect behavior: (1) players will behave closer to the equilibrium in the extensive form representation if they are sufficiently impatient and payoffs are sufficiently low; and (2) the representation effect exists depends on the number of decision periods (horizon). Experiment 1 uses a 2x2 design where the representations (extensive vs. strategic form) and the payoffs (high vs. low) are systematically varied. Experiment 2 manipulates the horizon of the game. DCH predicts when the horizon of the game is shorter, the representation effect detected in Experiment 1 will vanish. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.