Timing Games in Economics

这个项目探讨了经济学和博弈论中的时机问题。第一部分是关于定时游戏——玩家只需要决定何时停止的动态游戏。在经典的消耗战中，较晚的停止者享有更大的回报，而在先发制人的游戏中则相反。虽然文献可以追溯到20世纪50年代，但只分析了这些极端的案例。但在大多数经济背景下，成为第一或最后都是不可取的。这一部分介绍并充实了这类更大的基于等级奖励的定时游戏。该分析采用了全新的经济学工具，因为它开启了完全正函数理论。第二个时序项目分析了政治经济学中一个特定的时序博弈。枢纽投票理论的最新发展表明，一致的陪审团裁决是低效的。这一部分将陪审团的决定重新塑造为一个动态的故事，而不是一次投票，而是面对决策成本的个人投票。简单地说，如果延迟造成伤害，那么一致同意是信息上最优的规则。由此浮现的是一个丰富而可信的故事，即个人如何通过坚持己见（如动态拍卖理论）来表明其信息的强度，但后来又愿意在投票时模仿他人（与拍卖理论非常不同）而改变立场。最后一个政治经济学时间项目涉及决策理论。也就是说，在英国和加拿大这样的议会制民主国家，现任政府可以在任期届满前的任何时间举行选举。本课题建立了一种新的政府学习问题的连续时间贝叶斯模型；初步测试显示，预测结果与英国大选数据非常吻合。该理论的发展受到如何为金融中的看跌期权定价这一公开问题的启发；然而，选举时间是一个可更新的看跌期权。虽然前两个子项目是纯理论的，但这一部分也设想了一个数字方面，以及一些匹配。这个项目提供了一系列主要是实质性的和跨学科的进展。第一个项目提供了对“早起的鸟儿有虫吃，而先到的鸟儿没有”的模型的一般分析。这应该在整个社会科学领域产生广泛的影响和应用——从市场进入和投资决策（产业组织），到股市泡沫中的行为（金融学），或者赶时髦迟到的现象，或者加入时尚（社会学）。由于关于时间的决定通常是最简单的行业数据，可以毫无错误地观察到，因此这些应用程序应该具有许多经验内容。陪审团项目反驳了最近一个有影响力的理论论点，即一致的陪审团裁决是低劣的。分析还应该引入一个简单的框架来思考委员会中代价高昂的决策。选举时间安排项目展示了如何在政治经济学中运用金融理论的见解。它应该为有关新兴民主国家宪法改革的辩论提供信息，突出在任者在没有固定选举周期的情况下的优势。

This project explores issues of timing in economics and game theory. The first part concerns timing games - dynamic games where players need only decide when to stop. In the classic War of Attrition, later stoppers enjoy greater payoffs, while the reverse holds in the Pre-emption Game. While the literature dates back to the 1950's, only these extreme cases have been analyzed. But in most economic contexts, being first or last is not desired. This part introduces and fleshes out this larger class of timing games with general rank-dependent rewards. The analysis employs tools novel to economics, as it turns on the theory of Totally Positive functions. A second timing project analyzes a specific timing game in political economy. Recent developments in pivot voting theory suggest that unanimous jury verdicts are inefficient. This part recasts the jury decision not as a one-shot vote, but as a dynamic story of voting by individuals facing decision costs. Simply put, if delay hurts, then unanimity is the informationally optimal rule. What emerges is a rich and plausible story of how individuals' signal the strength of their information by holding out (as in dynamic auction theory), but later on are willing to switch sides of the vote parroting others (quite unlike auction theory). A final political economy timing project concerns decision theory. Namely, in parliamentary democracies like Britain and Canada, the incumbent government has the option to call an election any time before its term expires. This project sets up a novel continuous time Bayesian model of the government's learning problem; preliminary tests reveal a good predictive match against British election data. The theory developed is inspired by the open problem of how to price put options in finance; however, electoral timing is a renewable put option. While the first two subprojects are purely theoretical, this part also envisions a numerical side, as well as some matching. This project offers a range of mostly substantive and cross-disciplinary advances. The first project provides a general analysis of models where "the early bird gets the worm, but the first one does not." This should have a wide range of broad impacts and applications across the social sciences - from market entry and investment decisions (industrial organization), to behavior in stock market bubbles (finance), or the phenomenon of being fashionably late, or joining a fashion (sociology). Since decisions about timing are often the easiest bits of industry data that can be observed without error, these applications should have much empirical content. The jury project counters a recent influential theoretical arguments for the inferiority of unanimous jury verdicts. The analysis should also introduce a simple framework for thinking about costly decision-making in committees. The election timing project shows how to use insights from finance theory in political economy. It should inform the debate on constitutional reform in new democracies, highlighting the incumbent advantage without fixed election cycles.