Equilibrium Selection in Entry Games: An Experimental Study

本研究通过受雇受试者的受控实验室实验，检验了静态和动态进入游戏中的均衡选择概念。在进入游戏中，一组玩家中的每个人都会做出一个两难的决定：“进入”或“不进入”。进入的回报取决于选择进入的玩家的数量和状态变量Y，而不进入的回报不受其他人的进入决定或状态变量的影响。这项研究探索了完全信息进入游戏中的行为，在这种游戏中，所有参与者在做出动作选择之前都知道状态Y的值。这种博弈导致了多重均衡和协调问题。本研究的一个重点是评估两种不同均衡选择原则的预测能力。静态进入博弈被用来检验作为均衡选择工具的全局博弈理论。这一理论假设，玩家玩完全信息游戏，就像他们玩的是一个相关的全球不完全信息游戏。全局对策由所有对策的集合G组成，具有与感兴趣的对策相同的形式。玩全局游戏的策略涉及状态变量Y的阈值；如果Y大于或等于其阈值，则玩家选择进入，否则选择不进入。与原始的完全信息博弈及其多重均衡不同，全球不完全信息博弈具有唯一的完美贝叶斯均衡。因此，如果所有参与者都玩完全信息博弈，就好像有一个共同的理解，即所有参与者都会像玩相关的全局游戏一样玩那个游戏，那么协调问题就解决了。在动态进入博弈中，个人不仅决定是否进入，而且还决定何时进入。一旦进入，就是不可逆转的。已经进入的人数是州描述的一部分，个人可以根据该信息做出决定。动态进入游戏在n个时段后结束，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没有表明进入占主导地位，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。动态博弈中的这个进入门槛通常不同于同一个进入博弈的静态版本中的全局博弈门槛。这两个均衡选择原则中的任何一个实际上预测了个体群体在面对多重均衡造成的战略不确定性时的行为？该项目的创新之一是，它试图通过检查受控实验室环境中付费受试者的行为来解决这个问题。受试者内的实验设计能够评估在具有多个均衡的静态、完全信息进入游戏中的参与者的行为程度，就像他们在玩相关的全局游戏一样。动态游戏处理不仅是对子博弈完美均衡概念的测试，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以及如何与在同一游戏的静态版本中实现的协调程度不同。至于更广泛的影响，实验设计复制、建立和添加了关于这些重要问题的先前实验研究，并且足够简单，以至于其他研究人员应该能够复制和扩展发现。虽然该设计使用了一种进入博弈，这种博弈描述了金融市场的一些重要方面，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，例如合同和机制设计、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.