The Design of Optimal Social Interaction for Repeated Games

重复博弈理论是理解群体如何克服集体行动问题的重要工具。在这样的问题中，对个人来说最优的决策可能对群体来说不是最优的。所谓的“搭便车问题”表现在，例如，在寡头垄断行业中企图串通，在贸易谈判中企图实现多边关税削减，以及在自愿参与问题中需要集体努力时企图合作。 在重复博弈中，跨期制裁的使用可以用来重新调整个人激励与集体激励。众所周知，如果参与者有足够的耐心，在这些情况下可以维持集体最佳结果。 不幸的是，在许多情况下，球员没有耐心。在这些情况下，“充分合作”往往无法持续。 然而，确实存在这样的情况，在这种情况下，可以选择博弈中的互动模式，以最大限度地提高集体期望结果的可能性，这方面的一个例子是在公司的团队项目设计中。管理者必须根据公司低层管理者的特点来选择团队的规模和构成。一旦选择，个人的努力可以通过反复接触相互加强。另一个例子是住宅规划。邻国之间的局部溢出效应很常见。修剪草坪，让门廊的灯亮着，或者志愿维护公共花园都是积极溢出效应的例子。 一个对总人口特征有所了解的城市规划者必须在开发商的计划中做出选择，每个计划都提出了房屋的数量和空间安排。有些计划可能比其他计划更有利于促进“睦邻合作”。 这个项目研究了在确定哪种交互模式是最佳的过程中所涉及的权衡，以及答案如何取决于环境的细节。 在这种问题的最简单类型中，在每个时期，每个人都有一个“合作”和“不合作”或“搭便车”行动之间的二元选择。 该项目调查了群体的规模和群体内的社会联系程度如何影响实现社会理想的结果。该项目描述并研究了重复游戏的两种最佳互动模式。第一个限制了计划者对团体规模的选择。随机确定的折扣因子在总体中引入了未观察到的差异。一个计划者，只知道贴现因子的总体分布，选择群体规模m，以最大化群体的预期平均回报，给定群体内的预期战略互动。第二种模式概括了第一种模式，使规划者不仅可以确定群体规模，还可以确定群体内的社会联系模式。计划者的选择决定了溢出的模式和信息流的模式。本研究还分析了：（a）类型之间的相关性的影响（折扣因素）的个人，特别是当拥挤和拥挤发挥作用;（B）沟通的作用，作为一种方式，增加社会互动的最佳解决方案;均衡制裁的复杂性对最优互动模式的影响。

The theory of repeated games is a vital tool for understanding how groups overcome collective action problems. In such problems, decisions that are optimal for the individual may fail to be optimal for the group. So-called "free rider problems" manifest themselves, for example, in attempts to collude in oligopolistic industries, in attempts to achieve multilateral tariff reductions in trade negotiations, and in attempts to cooperate when group effort is required in voluntary participation problems. In repeated games, the use of intertemporal sanctions can be used to re-align individual incentives with collective incentives. It is well known that collectively optimal outcomes can be sustained in these cases if the participants are sufficiently patient. Unfortunately, in many cases the players are not patient. In these cases "full cooperation" often cannot be sustained. However, situations do exist in which the pattern of interaction in the game can be chosen to maximize the likelihood of collectively desirable outcomes.One example of this is found in the design of team projects in firms. A manager must choose the size and makeup of the team, given the characteristics of the pool of lower level managers at the firm. Once chosen, individual effort can be mutually enforced by repeated contact. Another example is in residential planning. Local spillovers between neighbors are common. Mowing the lawn, leaving one's porch light on, or volunteering to maintain communal gardens are examples of positive spillovers. A city planner who knows something about the aggregate population characteristics must choose among developers' plans, each of which proposes a number and spatial arrangement of houses. Some plans may be more conducive to facilitating "neighborly cooperation" than others. This project examines the tradeoffs involved in determining which interaction pattern is optimal, and how the answer depends on the particulars of the environment. In the simplest type of such a problem, in each period every individual has a binary choice between a "cooperative" and an "uncooperative" or "free-riding" action. The project investigates how the size of the group and the degree of social connectivity within the group matters for achieving socially desirable outcomes. The project describes and examines two models of optimal interaction for repeated play. The first limits a planner's choice to group size. Randomly determined discount factors introduce unobserved differences in the population. A planner, knowing only the aggregate distribution of discount factors, chooses group size m to maximize expected average payoff to the group, given the anticipated strategic interaction within the group. The second model generalizes the first to allow the planner to determine, not only group size, but also the pattern of social linkage within the group. The planner's choice determines both the pattern of spillovers and the pattern of information flows.The present project also extends the investigation to analyze: (a) the effect of correlation in the types (discount factors) of individuals, particularly when congestion and crowding play a role; (b) the role of communication as a way of increasing social interaction in the optimal solution; and (c) the effect of complexity of equilibrium sanctions on the optimal pattern of interaction.