Topics in Dynamic Games and Implementation Theory

该项目继续研究对严格分析经济动态、战略行为和社会选择极其有用的方法。具体的研究主题是(1)重复博弈中均衡的性质，其中行动是不可观察的，或者存在长期和短期参与者的混合；(2)重复博弈中的防重新谈判均衡；(3)马尔可夫均衡；以及(4)实现理论。对重复博弈的研究很重要，因为民间定理是寻找重复博弈数学解的最广泛使用的方法之一，它依赖于玩家观察其他玩家的行为与游戏结果之间的关系的假设。该项目的目的是研究当玩家观察到的结果不完全相关时，重复博弈中均衡的性质。在重复博弈中，合作源于参与者惩罚不合作行为的潜力。如果特工可以通过重新谈判避免惩罚，这种惩罚的威胁就会被打破。该项目继续研究在重复博弈中找到均衡的方法，这些博弈是不会重新谈判的。这条研究路线非常重要，因为强制要求均衡必须经过重新谈判，从而减少重复博弈的可能结果的数量，从而使经济理论家能够对动态经济过程的结果做出更准确的预测。该项目对马尔可夫策略的研究提供了另一种减少动态经济模型可能结果数量的方法。这项研究是基于这样一种观点，即策略只取决于一小部分相关的过去变量，而不是整个游戏历史。本项目首次提出了这些受限或马尔可夫策略的一般定义，并研究了它们的特点。实施论关注的问题是，什么时候才有可能设计一个博弈或“机制”，其均衡具有相对于给定的社会福利标准是可取的性质。传统的执行理论认为，结果可以由中央当局强制执行。该项目将实现理论扩展到某些个人的行为无法被其他任何人观察的情况。这个项目应该得到支持，因为它对经济理论做出了根本性的贡献。许多动态经济模型具有巨大的均衡集合，这一事实阻碍了经济分析。这项研究的结果可能使理论家能够对这些模型的结果做出更具区分性的预测。

This project continues research on methods that are extremely useful for rigorously analyzing economic dynamics, strategic behavior and social choice. The specific research topics are (1) the nature of equilibrium in repeated games where actions are not observable or where there is a mixture of long- and short-run players; (2) renegotiation- proof equilibria in repeated games; (3) Markov equilibrium; and (4) implementation theory. The research on repeated games is important because the Folk Theorem, one of the most widely used methods for finding mathematical solutions to repeated games, depends on the assumption that players observe a relationship between the actions of the other players and the outcomes of the games. The purpose of the project is to study the nature of equilibrium in repeated games when the outcomes observed by the players are imperfectly correlated. In a repeated game, cooperation derives from the potential of players to punish non-cooperative behavior. This threat of punishment breaks down, if agents can avoid the punishment by renegotiation. The project continues to study ways of finding equilibria in repeated games that are renegotiation-proof. This line of research is very important because imposing a requirement that equilibria be renegotiation-proof reduces the number of possible outcomes to repeated games in this way enabling economic theorists to make more precise predictions about the outcomes of dynamic economic processes. The project's research on Markov strategies offers another way of reducing the number of possible outcomes of dynamic economic models. The research is based on the idea that strategies depend on only a small set of relevant past variables rather than on the entire history of the game. This project formulates for the first time a general definition of these restricted or Markov strategies and studies their characteristics. Implementation theory is concerned with the question of when it is possible to design a game or "mechanism" whose equilibria have properties that are desirable with respect to a given criterion of social welfare. Traditional implementation theory assumes that the outcome can be enforced by a central authority. This project extends implementation theory to situations where some individuals' actions cannot be observed by anyone else. This project should be supported because it makes fundamental contributions to economic theory. Economic analysis has been hindered by the fact that many dynamic economic models have huge sets of equilibria. The results of this research could enable theorists to make more discriminating forecasts of the outcomes of these models.