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，对个人来说是最优的决策可能对群体来说不是最优的。例如，所谓的“搭便车问题”表现为企图在寡头垄断工业中串通，企图在贸易谈判中实现多边关税削减，企图在需要集体努力时在自愿参与问题上进行合作。在重复博弈中，可以使用跨期制裁来重新调整个人激励与集体激励。众所周知，在这些情况下，如果参与者有足够的耐心，集体最佳结果是可以持续的。不幸的是，在很多情况下，球员都没有耐心。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，即游戏中的互动模式可以被选择以最大化集体期望结果的可能性。这方面的一个例子可以在公司团队项目的设计中找到。经理必须根据公司中较低级别的经理的特点，选择团队的规模和组成。一旦被选中，个人的努力就可以通过反复接触而相互加强。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，让门廊的灯开着，或者自愿维护公共花园都是积极溢出效应的例子。一个对人口总量特征有所了解的城市规划者必须在开发商的规划中做出选择，每个规划都提出了房屋的数量和空间安排。有些方案可能比其他方案更有利于促进“睦邻合作”。这个项目检查了在确定哪种交互模式是最佳的过程中所涉及的权衡，以及答案如何依赖于环境的细节。在这种问题的最简单类型中，在每个时期，每个人都有“合作”和“不合作”或“搭便车”行为之间的二元选择。该项目调查了群体的规模和群体内部的社会联系程度对实现社会理想结果的影响。该项目描述并检验了重复游戏的两种最佳交互模式。第一个限制了计划者对团队规模的选择。随机确定的贴现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收益，给定群体内预期的战略互动。第二个模型概括了第一个模型，使规划者不仅可以确定群体规模，还可以确定群体内社会联系的模式。计划者的选择既决定了溢出的模式，也决定了信息流的模式。本项目还将调查扩展到分析：(a)个体类型（折扣因子）的相关性影响，特别是当拥堵和拥挤起作用时；(b)沟通作为一种增加社会互动的方式在最佳解决方案中的作用；(c)平衡制裁的复杂性对最优交互模式的影响。

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.