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

行为经济学的主要目标之一是更好地理解在与经济、社会和政治竞争相关的战略环境中，人类认知限制对行为的影响。行为经济学的这一分支，行为博弈论，关注的是人们如何在战略环境中对其他个体的预期行为形成预期。这个项目将实验性地研究“脏脸游戏”，这是一个战略环境的典型例子，在这个环境中，个人可以观察到游戏中其他玩家的一些行为，从而使他们能够做出推断，从而做出更明智的决定。这是一款简单但具有说明性的游戏，它模拟了人们根据他人过去的行为更新自己的信念并做出决定的情况，例如通过阅读他人的评论来选择餐馆或购买新产品。关于博弈行为的经典理论，基于完美理性的假设，在这个博弈中做出了行为上不可信的预测。放松完美理性假设会导致对脏脸游戏中行为的预测发生巨大差异，这使其成为新的“动态认知层次理论”（DCH）的理想测试平台，该理论预测，在脏脸游戏中，玩家在两种不同的传统实验协议（直接反应与策略方法）下通常会表现不同，而标准理论没有预测任何行为差异。本项目设计了两个实验来检测DCH在这些游戏中预测的行为差异。该项目的长期目标不仅是检验这一理论，而且还为考虑到认知局限性的政策设计提供见解。有了改进的理论模型，政策制定者可以设计出认知上更稳健的拍卖、税收计划、监管和其他机制，以改善经济表现。脏脸游戏是一种战略环境，在这种环境中，一群人中的每个人要么有一张脏脸，要么有一张干净脸，他们可以看到所有其他玩家的脸，但看不到自己的脸。在一系列的决策周期中，每个个体都可以采取行动，提供一些关于他们所看到的面孔的信息，每个个体的最终目标是通过观察其他人的行动来了解自己的面孔类型。在游戏开始时，观察者会诚实地宣布是否至少有一张脏脸。从标准博弈论的角度来看，玩家最终会知道他们的脸是脏还是干净。此外，该博弈的广泛形式表征和战略形式表征在战略上是等价的，并做出了相同的经典预测。然而，从心理学的角度来看，心理过程是完全不同的——在战略形式表征中，玩家根据假设的事件进行推理，而在广泛形式表征中，玩家可以根据观察到的行为进行统计推断。在两个人的“脏脸”游戏中，均衡理论预测玩家将在两段时间内知道自己的脸类型——不管回报和表现（广泛形式vs.策略形式）如何。具体而言，DCH预测了收益结构和博弈形式表征会共同影响行为：(1)当玩家足够不耐烦且收益足够低时，他们会在广泛形式表征中表现得更接近均衡；(2)表征效应的存在取决于决策周期（视界）的数量。实验1使用2x2设计，其中表现形式（广泛vs.策略形式）和回报（高vs.低）是系统变化的。实验2操纵游戏的视界。DCH预测当游戏视界变短时，在实验1中检测到的表征效应将消失。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.