Dynamic Elicitation of Unobservable Information

动态获取不可观察信息

• 批准号: 1426867
• 负责人: Christopher Chambers
• 金额: $ 8.74万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1426867&HistoricalAwards=false
• 关键词: Dynamic; Elicitation; Unobservable; Information

Most aspects of real-world decision making involve two complicating factors: uncertainty and time. The proposed research applies very broadly, but we can think of investment decisions. For example, the behavior of the stock market is largely unpredictable throughout time, and depends on many factors, many of which are not understood to lay investors. All the same, real-world decision makers are forced to make decisions in such environments. Individuals are required to choose an investment portfolio for their retirement without knowing how capital markets will fare. There are experts who are in a much better position to understand the uncertainty. These individuals are likewise more likely to recognize the importance of events occurring throughout time. For example, a professional investor may recognize when a certain stock becomes under or overvalued; and thus may revise her assessment as to the likely future performance of the stock. The proposed research seeks to construct a device which will allow the lay investor to uncover all information which the professional deems relevant throughout time. The device works by providing monetary incentives to the professional. It can be understood as a compound option. For example, an option written on Tuesday gives the individual the right to choose any of a given collection of securities on Wednesday. The value of each security depends on the uncertainty in question. A compound option written on Monday gives the individual the right to choose any of a given collection of options on Tuesday. By utilizing such a simple device, we propose to establish that a completely uninformed investor can induce the professional investor to reveal everything she knows about the behavior of the market, including how she perceives it will behave in the future at all future dates. No payments need be given to the professional until all uncertainty is resolved. Further, the payments can be chosen to be very small.Formally, we propose to adapt the notion of a proper scoring rule to a dynamic situation. An expert holds subjective probabilistic beliefs about a future state of the world, and also receives a sequence of signals as to the true state. These signals are observed throughout time. It is without loss to imagine that the expert holds a probability over probabilities, say, when there is one intermediate signal realization. The goal is to elicit this probability tree throughout time, as it is realized. All payoffs only occur after the state of the world obtains. We show how to construct a function, which at each stage, strictly induces the expert to announce their one-step-ahead belief. Results are obtained in both discrete and continuous time, and moreover, we propose to show that the class of mechanisms so constructed exhausts the class of all incentive compatible mechanisms.

现实世界的决策大多涉及两个复杂的因素：不确定性和时间。 建议的研究适用范围非常广泛，但我们可以考虑投资决策。 例如，股票市场的行为在很大程度上是不可预测的，并取决于许多因素，其中许多是不了解外行投资者。 尽管如此，现实世界的决策者还是被迫在这样的环境中做出决策。 个人需要在不知道资本市场将如何发展的情况下为自己的退休生活选择一个投资组合。 有些专家更能理解这种不确定性。 这些人同样更有可能认识到整个时间发生的事件的重要性。 例如，一个专业投资者可能会认识到某只股票何时被低估或高估，因此可能会修改她对该股票未来可能表现的评估。 拟议的研究旨在构建一种设备，使外行投资者能够发现专业人士认为相关的所有信息。 该装置通过向专业人员提供金钱激励来发挥作用。 可以理解为复合期权。 例如，周二卖出的期权赋予个人在周三选择任何给定证券集合的权利。 每种证券的价值取决于所涉及的不确定性。 在星期一卖出的复合期权，使个人有权在星期二选择给定的期权集合中的任何一个。 通过使用这样一个简单的方法，我们建议建立一个完全不知情的投资者可以诱导专业投资者透露她所知道的关于市场行为的一切，包括她如何看待它将在未来的所有日期表现。 在所有不确定性得到解决之前，不需要向专业人员支付任何款项。 此外，付款可以选择是非常小的。形式上，我们建议适应的概念，一个适当的评分规则的动态情况。 专家对世界的未来状态持有主观的概率信念，并且还接收关于真实状态的一系列信号。 这些信号在整个时间内都被观察到。 假设存在一个中间信号实现时，专家持有一个概率高于概率的概率，这是毫无损失的。 我们的目标是在整个时间内得出这个概率树，因为它是实现的。 所有的收益都只发生在世界的状态得到之后。 我们展示了如何构建一个函数，在每个阶段，严格诱导专家宣布他们的一步领先的信念。 结果得到在离散和连续的时间，而且，我们建议表明，这样构造的机制类用尽类的所有激励相容的机制。