Continuous-time games with asynchronous moves: Theory and applications

该奖项资助了重复战略互动理论的新研究，也被称为重复博弈理论。事实证明，博弈论的这一分支在经济学和其他社会科学领域都具有巨大的影响力。过去的研究对我们思考社会中个人之间的合作、市场上的反复竞争或国际治理等重要问题的方式产生了革命性的影响。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，在许多长期互动的现实世界中，参与者一次只采取一个行动，因此这些行动的确切时间表现出一些随机性。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，并将该模型应用于特定的经济和社会背景。这些应用涵盖了许多不同的主题，如立法议价、在线拍卖和寡头垄断竞争。新的方法论工具将提供方法来解决难以使用更标准的模型来回答的研究问题，并为新的研究方向铺平道路。该奖项资助了三个不同的研究项目。项目一：研究团队研究动态游戏，在这种游戏中，玩家只能在离散的随机时间修改自己的行动，而他们根据当前阶段游戏中指定的行动不断积累收益。研究人员表示，这些游戏与标准的同步移动重复游戏相比，在有限和无限的时间范围内都表现出了重要的差异。例如，对于固定的有限视界，即使阶段博弈具有独特的非合作纳什均衡，在大多数时间范围内也可能存在意味着合作的均衡。该团队提供了一个无限视界博弈的例子，其中任何阶段博弈的静态均衡的重复都不是动态博弈的均衡，所有静止子博弈的完美均衡（sspe）都包含非平凡的动态。该团队已经确定了sspe的普遍存在（对于任何贴现率），并描述了随着玩家变得无限耐心，所有sspe收益的极限集。“项目二”采用该框架来调查ebay等二手价格在线拍卖，在这种情况下，竞标者并不持续参与拍卖，而是获得随机的、离散的出价或修改出价的机会。该团队表明，即使估值是私人的，竞标者可以离开代理出价，这些博弈除了真实出价外，还有许多不同的弱非主导策略均衡。这些均衡可以包括逐步出价，并等到拍卖结束后才开始出价。这些结果与我们在各种在线拍卖中观察到的行为一致。第三项目延续了PI之前在连续时间随机识别多边谈判方面的工作。该团队正在将分析扩展到空间政策结果的讨价还价，其中一个重要应用是立法议价，当立法者之间无法进行货币转移时。他们主要关注的是，在谈判时间很长的情况下，确定预期的政策如何取决于现状的结果和各方承认的可能性。在项目的另一部分，他们使用联盟议价模型的平等到达规范来提出一个非合作建立的合作解决方案概念。更广泛的影响包括社会科学学科的学者使用这些新方法，更好地了解在线拍卖的特性，以及对一些研究生进行这些新研究方法的培训。

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.