Continuous-time games with asynchronous moves: Theory and applications

该奖项资助重复战略互动理论的新研究，也被称为重复博弈理论。 博弈论的这一分支已被证明在经济学和其他社会科学中具有巨大的影响力。 过去的研究在我们思考社会中个人之间的合作、市场中的重复竞争或国际治理等重要主题方面产生了变革性的影响。 目前对这种重复互动进行建模的方法最适用于每个阶段的参与者同时做出选择的情况。然而，在许多长期交互的真实的世界情境中，参与者一次一个地采取动作，使得这些动作的确切时间表现出某种随机性。研究者开发了一种新的方法来模拟这种情况，旨在获得一般的理论见解，并将模型应用于特定的经济和社会背景。这些应用涉及许多不同的主题，如立法谈判、在线拍卖和寡头垄断竞争。 新的方法工具将提供解决难以使用更标准模型回答的研究问题的方法，并为新的研究方向铺平道路。该奖项资助三个不同的研究项目。 项目一：该研究小组研究了动态游戏，其中玩家只能在离散的随机时间修改他们的行动，而他们根据阶段游戏中当前指定的行动不断积累收益。 研究人员表明，这些游戏表现出重要的差异，相对于标准的同时移动重复游戏，无论是在有限和无限的时间范围。例如，在固定的有限时间范围内，即使阶段博弈有唯一的非合作纳什均衡，也可能存在意味着大部分时间范围内合作的均衡。该团队提供了一个无限水平博弈的例子，其中重复阶段博弈的任何静态均衡都不是动态博弈的均衡，并且所有静态子博弈完美均衡（sspe）都涉及非平凡的动态。 该团队已经建立了一般存在的sspe（任何折扣率），并正在表征的极限集的所有sspe的回报，球员成为patient.Project二适应的框架，调查第二价格网上拍卖，如易趣，当投标人不参加连续的拍卖，而是随机离散的机会，放置或修改出价。 该团队表明，即使当估值是私人的，投标人可以离开代理出价，这些游戏有许多不同的均衡弱非支配策略，除了真实的出价。这些均衡可能涉及逐步出价，直到拍卖结束才开始出价。 这些结果与我们在各种在线拍卖中观察到的行为是一致的。项目三延续了PI以前在连续时间随机识别多边讨价还价方面的工作。 该小组正在将分析扩展到空间政策结果的谈判，其中一个重要的应用是立法谈判，当立法者之间不能进行货币转移时。他们的主要重点是确定预期的政策如何取决于现状的结果和球员的认可概率，当谈判的时间跨度很长。在该项目的另一部分，他们正在使用他们的联盟谈判模型的平等到达规格，提出了一个非合作建立的合作解决方案的概念，更广泛的影响，包括使用这些新方法的学者在社会科学学科，更好地了解网上拍卖的属性，并在这些新的研究方法的几个研究生的培训。

This award funds new research in the theory of repeated strategic interactions, also known as the theory of repeated games. This branch of game theory has proven to be enormously influential both in economics and other social sciences. Past research has been transformative in its effect on, in the way we think about cooperation among individuals in a society, repeated competition in markets, or international governance, among other important topics. The current method for modeling this kind of repeated interaction applies best to situations in which participants in each period make simultaneous choices. However, in many real world situations of long-term interaction, participants take actions one at a time, such that the exact time of these actions exhibit some randomness. The investigator develops a new method for modeling such situations, aiming to obtain general theoretical insights and to applying the model in specific economic and social contexts. These applications range through many different topics, such as legislative bargaining, online auctions and oligopoly competition. The new methodological tools will offer ways to address research questions that are too difficult to answer using more standard models and pave the way for new research directions. The award funds three distinct research projects. Project One: The research team investigates dynamic games in which players can only modify their actions at discrete random times, while they accumulate payoffs continuously according to the currently specified actions in a stage game. The researchers show that these games exhibit important differences relative to standard simultaneous move repeated games, both on finite and infinite time horizons. For example, with fixed finite horizon, there can be equilibria implying cooperation for most of the time horizon, even when the stage game has a unique noncooperative Nash equilibrium. The team provides an example of an infinite horizon game in which repetition of any of the static equilibria of the stage game is not an equilibrium of the dynamic game, and all stationary subgame perfect equilibria (sspe) involve nontrivial dynamics. The team has established the general existence of sspe (for any discount rate), and are characterizing of the limit set of all sspe payoffs as players becomeinfinitely patient.Project Two adapts the framework to investigates second-price online auctions like ebay, when bidders do not participate continuously at the auction, but instead receive random discrete opportunities to place or modify bids. The team shows that even when valuations are private and bidders can leave proxy bids, these games have many different equilibria on weakly undominated strategies, besides truthful bidding. These equilibria can involve gradual bidding, and waiting till the end of the auction to start placing bids. These results are consistent with the behavior we observe in a variety of online auctions.Project Three continues the PI's previous work on continuous-time random recognition multilateral bargaining. The team is extending the analysis to bargaining over spatial policy outcomes, an important application of which is legislative bargaining when there cannot be monetary transfers among legislators. Their primary focus is identifying how the expected policy depends on the status quo outcome and the recognition probabilities of players, when the time horizon for negotiations is long. In another part of the project they are using the equal arrivals specification of their coalitional bargaining model to propose a noncooperatively founded cooperative solution concept.Broader impacts include the use of these new methods by scholars across the social science disciplines, better understanding of the properties of online auctions, and the training of several graduate students in these new research methods.