Equilibrium Selection in Entry Games: An Experimental Study

本研究考察了静态和动态进入博弈中的均衡选择概念，使用了付费人类受试者的受控实验室实验。在进入博弈中，一组玩家中的每个成员都要做出一个二元决策：“进入”或“不进入”。进入的收益取决于选择进入的玩家数量和状态变量Y，而不进入的收益则与其他人的进入决策或状态变量无关。该研究探讨了完全信息博弈中的行为，在完全信息博弈中，所有参与者在做出行动选择之前就知道状态Y的值。这种博弈产生了多重均衡和协调问题。本研究的一个特别重点是评估两种不同均衡选择原则的预测能力。静态进入博弈作为一种均衡选择手段，用于检验全局博弈理论。这一理论认为，玩家玩完全信息的游戏，就好像他们在玩一个相关的不完全信息的全球游戏。全局博弈由所有博弈的集合G组成，其形式与感兴趣的博弈相同。玩全局博弈的策略包含状态变量Y的阈值；如果Y大于或等于他们的阈值，玩家选择进入，否则选择不进入。与原始的完全信息博弈具有多重均衡不同，不完全信息全局博弈具有唯一的完美贝叶斯均衡。因此，如果所有玩家都在玩完全信息游戏，就好像所有玩家都在玩相关的全球游戏一样，那么协调问题就解决了。在动态进入博弈中，个体不仅决定是否进入，而且决定何时进入。一旦进入就不可逆了。已经进入的人数是状态描述的一部分，个人可以根据该信息做出决定。动态进入游戏在n个周期后结束，或者当每个玩家都选择进入时结束，以先到者为准。在这种情况下，子博弈完美是相关的均衡选择手段。如果状态变量Y不表明进入处于劣势，则子博弈完美均衡预测要求所有参与者立即选择进入，从而解决协调问题。动态游戏中的进入门槛通常不同于相同进入游戏的静态版本中的全局游戏门槛。这些均衡选择原则中的任何一个，真的能预测个体群体在面对多重均衡所产生的战略不确定性时的行为吗？这个项目的一个创新之处在于，它试图通过在受控的实验室环境中检查付费受试者的行为来解决这个问题。主体内实验设计能够评估玩家在静态的、完整的信息输入游戏中的多重均衡行为，就像他们在玩一个相关的全局游戏一样。动态博弈处理不仅是对子博弈完美均衡概念的检验；更重要的是，它能够评估在动态结构下实现的协调程度是否与在同一游戏的静态版本中实现的协调程度不同以及如何不同。至于更广泛的影响，实验设计复制，建立和增加了先前对这些重要问题的实验研究，并且足够简单，其他研究人员应该能够复制和扩展这些发现。虽然该设计使用了一个描述金融市场某些重要方面的入门游戏，但理解人们在存在多种均衡的情况下的行为在其他领域也非常重要，例如契约和机制设计，标准和惯例的起源以及自我实现预言的可能性。

This study examines equilibrium selection concepts in static and dynamic entry games using controlled laboratory experiments with paid human subjects. In an entry game, each member of a group of players makes a binary decision: "enter" or "don't enter." The payoff to entry depends on the number of players who choose to enter and on a state variable Y, while the payoff to non-entry is invariant to entry decisions by others or the state variable. The study explores behavior in entry games of complete information, where the value of the state Y is known to all players in advance of making their action choices. Such games give rise to multiple equilibria and coordination problems. A particular focus of this study is to assess the predictive power of two different equilibrium selection principles.Static entry games are used to test the theory of global games as an equilibrium selection device. This theory posits that players play games of complete information as if they were playing a related global game of incomplete information. The global game consists of the set of all games, G, with the same form as the game of interest. The strategy for playing a global game involves a threshold value for the state variable Y; players choose to enter if Y turns out to be greater than or equal to their threshold value and choose not to enter otherwise. Unlike the original game of complete information with its multiplicity of equilibria, the global game of incomplete information has a unique perfect Bayesian equilibrium. Therefore, if all players play the game of complete information as though there were a common understanding that all players will play that game as if they were playing the related global game, the coordination problem is resolved.In dynamic entry games, individuals decide not only whether to enter but also when to enter. Once entry occurs it is irreversible. The number of people who have already entered is part of the state description, and individuals can condition their decisions on that information. The dynamic entry game ends after n periods, or when every player has chosen to enter, whichever comes first. In this setting, subgame-perfection is the relevant equilibrium selection device. If the state variable, Y, does not indicate that entry is dominated, the subgame-perfect equilibrium prediction calls for all players immediately to choose to enter, thereby resolving the coordination problem. This entry threshold in the dynamic game will generically differ from the global game threshold in static versions of the same entry game.Do either of these equilibrium selection principles actually predict how groups of individuals behave in the face of strategic uncertainty created by a multiplicity of equilibria? One of the innovations of this project is that it seeks to address this question by examining the behavior of paid subjects in a controlled laboratory environment. Within-subject experimental design enables the assessment of the extent to which players in static, complete information entry games with multiple equilibria behave as though they were playing a related global game. Dynamic game treatment not only serves as a test of the subgame-perfect equilibrium notion; more importantly, it enables the assessment of whether and how the degree of coordination achieved under the dynamic structure differs from that achieved in static versions of the same game.As for broader impacts, the experimental design replicates, builds on and adds to prior experimental research on these important questions and is simple enough that other researchers should be able to replicate and extend the findings. While the design uses an entry game that characterizes some important aspects of financial markets, an understanding of how people behave in situations where there are a multiplicity of equilibria is of great importance in other areas as well, such as contract and mechanism design, the origin of standards and conventions and the possibility of self-fulfilling prophecies.