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.

现实世界决策的大多数方面都涉及两个复杂因素：不确定性和时间。 拟议的研究非常广泛地适用，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无法预测的，并且取决于许多因素，其中许多因素不理解为外行投资者。 同样，现实世界中的决策者被迫在这种环境中做出决策。 个人必须选择投资组合以进行退休，而不知道资本市场的表现。 有些专家在理解不确定性方面处于更好的位置。 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，专业投资者可能会认识到某个股票何时被高估或高估；因此，可能会对她的评估对股票的未来业绩进行评估。 拟议的研究试图构建一种设备，该设备将使外行投资者能够发现专业人士认为在整个时间内相关的所有信息。 该设备通过向专业人士提供货币激励措施来起作用。 它可以理解为复合选项。 例如，周二撰写的选项使个人有权在周三选择任何给定的证券收藏。 每个安全性的价值取决于所讨论的不确定性。 周一编写的复合选项使个人有权在星期二选择任何给定的选项集合。 通过利用如此简单的设备，我们建议确定一个完全不知情的投资者可以诱使专业投资者揭示她对市场行为的了解，包括她将来将来将来会表现出来。 在解决所有不确定性之前，不需要向专业人员付款。 此外，可以选择付款非常小。从表面上看，我们建议将适当的评分规则的概念适应动态情况。 专家对世界未来状态保持主观概率信念，并收到有关真实状态的一系列信号。 这些信号在整个时间内都观察到。 想象专家在一个中间信号实现时，专家认为概率具有概率。 目的是在实现的过程中启动这种概率树。 所有的收益仅在世界状态获得后才发生。 我们展示了如何构建一个功能，在每个阶段，都严格诱使专家宣布其一步前的信念。 结果均在离散时间和连续时间中获得，而且我们建议表明，如此构建的机制类别耗尽了所有激励兼容机制的类别。