Experimental analysis of the role of higher-order beliefs about the cognitive abilities of others in coordination games

通过这个项目，我们的目标是更好地理解在金融市场或银行挤兑等战略情况下协调失败的可能原因。约翰·梅纳德·凯恩斯（1936）在他著名的选美比赛类比中认为，一个好的投资策略与其说取决于对各种资产的基本价值有正确的评估，不如说是取决于你相信别人相信的基本价值是什么，以及你相信别人相信的基本价值是什么，等等，可能无穷无尽。简而言之，投资者玩的游戏首先是一种协调游戏，在这种游戏中，“高阶信念”起着至关重要的作用。有一篇文献（在提案中引用）表明，从理论上讲，协调博弈的结果对于个人高阶信念的微小变化是多么脆弱。另一方面，也有实验文献（在提案中引用）表明，现实生活中的大多数玩家并不采用高阶信念。后一种文献主要关注两个方面，即风险优势（“低风险”）和帕累托优势（“高收益”）之间的权衡，以及关于收益的不完全信息在游戏中的作用。我们希望通过研究基于不完善认知的第三个战略不确定性来源来加深对这个问题的理解：并非每个玩家都必须完全掌握所有可能的选择。从理论上讲，理性玩家的行为取决于他对对手认知能力的高阶信念（包括对手对自己认知能力的高阶信念）。为了测试玩家是否具有这种性质的高阶信念，我们建议基于Blume和Gneezy（2000年，2010年）的工作进行一个专门针对这一目的的实验。在他们的实验设计中，受试者玩协调游戏，其中最佳的协调方式并不明显。他们有两种处理方式：1)一个玩家与自己进行协调游戏，2)两个玩家进行协调游戏。他们发现许多受试者在1)中表现最佳，但在2)中表现不佳。他们的解释是，实验对象对对手的认知能力过于悲观。我们计划添加第三种处理(3)，当她的对手和自己对弈时（就像处理1中一样），感兴趣的玩家被要求赌她对手的选择。对对手的认知能力持悲观态度的玩家会在2)和3)中选择次优策略，而具有非平凡高阶信念的玩家可能会在2)中选择次优策略，但打赌对手会在3)中选择最优策略。因此，我们可以通过实验确定协调失败的主要原因是玩家有悲观的简单信念，还是因为他们的高阶信念。

With this project we aim to provide a better understanding of the possible reasons of coordination failure in strategic situations such as financial markets or bank runs.John Maynard Keynes (1936) in his famous beauty contest analogy argues that a good investment strategy not so much depends on having the correct assessment of the fundamental value of the various assets, but more so on what one believes others believe what the fundamental value is and what one believes others believe what others believe the fundamental value is, and so on, possibly ad infinitum. In short, the game investors play is foremost a coordination game and in such games "higher order beliefs" play a crucial role.There is a literature (cited in the proposal) that shows, in theory, how fragile the outcome of coordination games is with respect to small changes in individuals' higher order beliefs. On the other hand there is also an experimental literature (cited in the proposal) that demonstrates that most players in real life do not employ beliefs of high order. This latter literature focuses on two aspects, the tradeoff between risk-dominance ("less risky") and Pareto-dominance ("higher payoffs") and the role of imperfect information about the payoffs in the game.We want to add to the understanding of this problem by investigating a third source of strategic uncertainty based on imperfect cognition: not every player necessarily fully grasps all the possible choices at her disposal. Theoretically, a rational player's behavior then depends on all her higher-order belief about her opponents' cognitive ability (including her opponent's higher order beliefs about her own cognitive ability). In order to test whether players have higher-order beliefs of this nature, we propose to run an experiment tailored for this purpose that builds on the work by Blume and Gneezy (2000, 2010). In their experimental design subjects play coordination games, in which the optimal way to coordinate is not immediately obvious. They have two treatments: 1) a single player plays the coordination game against herself, 2) two players play the coordination game. They find that many subjects play optimally in 1) but not in 2). Their explanation is that subjects are overly pessimistic about their opponents' cognitive ability.We plan to add a third treatment 3) while her opponent plays the game against himself (as in treatment 1), the player of interest is asked to bet on her opponent's choices.A player with pessimistic beliefs about his opponents' cognitive ability will choose the suboptimal strategy in 2) and 3), while a player with non-trivial higher-order beliefs may choose the suboptimal strategy in 2) but bet that her opponent will choose optimally in 3). We can, thus, experimentally identify whether the main reason for coordination failure is that players have pessimistic simple beliefs, or whether it is because of their higher-order beliefs.