Collaborative Research on Multi-dimensional Models of Bargaining and Elections

集体选择理论的发展是为了促进我们对群体决策的理解，特别是当一个群体的决策影响到所有成员时，也许不是同等的。这种情况充满了谈判、联盟形成和其他形式的复杂战略互动的机会。该理论对决策的程序性细节进行了抽象，因此是相当普遍的。不幸的是，阿罗(1963)、普洛特(1967)、斯科菲尔德(1983)和其他人已经表明，“核心”要点--任何联盟都不能迫使有利可图的改变--往往是不存在的。此外，McKelvey(1977,1979)已经证明，当核心是空的时，通过连续的联盟行动可以达到的社会选择构成了整个选择空间。这促使一些人(例如Riker(1980))得出结论，集体决策本质上是不稳定和不可预测的。在这项提案中，我们概述了一个关于谈判和选举的研究计划，目的是促进我们对集体选择的理解。尽管我们的工作与集体选择理论有联系，但我们的方法是独特的：我们明确地对做出集体选择的制度设置进行建模，例如立法机构或选举的程序规则。一旦明确了选择的制度背景，就可以应用非合作博弈论的工具，将选择作为非合作博弈中均衡行为的产物进行分析。我们的模型有几个共同的元素，允许进行统一的理论处理：它们是动态的和多维的，而聚集个人偏好的主要机制是投票。我们试图发展一个一般理论，为未来的理论和应用工作奠定基础，因此，我们的重点主要是静态均衡(一种特别简单的形式的均衡)的存在以及与集体选择理论的联系。我们相信，解决这些基础性问题将有助于未来分析更具体的模型，允许更清晰的均衡表征、比较静力学分析、计算分析和经验测试。该提案由两部分组成，分别载于第2节和第3节。在第2节中，我们提出了五个关于讨价还价研究的项目，概述如下。第一个项目的结果包含在Banks and Duggan(1998)中，并且接近最终的形式。集体选择的讨价还价模型：我们在基本模型中建立了静态均衡的存在性和稳健性，并推广了过去关于讨价还价的工作。我们建立了我们的非合作理论准确预测核心的条件，从而印证了集体选择理论。格陵兰的多维模型：我们在基本模型中考察现状的稳定性问题。我们的模型推广了Kreshbiel(1996,1998)的立法僵局模型，并提供了以下见解：在多维环境下，Krehbiel模型中的完全僵局是罕见的，尽管部分类型的僵局是可能的。同时讨价还价：我们将均衡存在的结果推广到一个多群体同时讨价还价的模型。应用领域包括研究联邦政府体系、两院制立法机构、不同公司内部的决策，以及不同国家议会内的决策。经济环境中的讨价还价：我们捕捉经济背景下的讨价还价，给予决策者关于它们的天赋和财产权，并允许天赋随时间随机变化。我们主要研究均衡存在性和核心等价。动态集体选择：我们允许在达成协议后继续讨价还价--一个时期的讨价还价结果成为下一个时期讨价还价的现状点。我们试图克服“持续”集体选择模型中均衡存在分析中的技术难题。在第三节中，我们建议研究重复选举，并通过允许多维政策空间和更一般的偏好来推广Duggan(1997)。选举模型在数学上与我们的基本讨价还价模型非常相似，我们在分析讨价还价时开发的技术使我们能够确定静态选举均衡的存在，刻画它们的特征，并澄清它们与核心的联系。

A theory of collective choice is developed to facilitate our understanding of group decisionmaking, particularly when the decision of a group affects all members, perhaps not equally. Such situations are rife with opportunities for negotiation, coalition formation, and other forms of complex strategic interaction. The theory abstracts for the procedural details of decisionmaking and is, therefore, quite general. Unfortunately, Arrow (1963), Plott (1967), Schofield (1983) and others have shown that "core" points -- points from which no coalition can force a profitable change -- often fail to exist. Moreover, McKelvey (1977, 1979) has shown that, when the core is empty, the social alternatives that can be reached by successive coalitional moves comprise the entire space of alternatives. This has prompted some (e.g., Riker (1980)) to draw the conclusion that collective decisionmaking is inherently unstable and unpredictable. In this proposal, we outline a research program on bargaining and elections with the goal of advancing our understanding of collective choice. Although our work has connections to the theory of collective choice, our approach is distinct: we explicitly model the institutional setting in which collective choices are made, such as the procedural rules of legislatures or elections. Once the institutional context of choice is clarified, the tools of non-cooperative game theory can be applied, and choices can be analyzed as the product of equilibrium behavior in non-cooperative games. Our models have several elements in common that permit a unified theoretical treatment: they are dynamic and multi-dimensional, and the primary mechamisn by which individual preferences are aggregated is voting. We attempt to develop a general theory that will lay the groundwork for future theoretical and applied work and, accordingly, our focus is primarily on the existence of stationary equilibria (equilibria of a particularly simple form) and on connections to the theory of collective choice. We believe that addressing these foundational issues will facilitate future analysis of more highly specified models, allowing sharper equilibrium characterizations, comparative statics analysis, computational analysis, and empirical testing. The proposal consists of two parts, presented in Sections 2 and 3. In Section 2, we propose five projects on the study of bargaining, as outlined below. The results of the first project are contained in Banks and Duggan (1998), and are near their final form.A Bargaining Model of Collective Choice: We establish existence and robustness of staionary equilibria in the basic model, and generalize past work on bargaining. We establish conditions under which our non-cooperative theory predicts precisely the core, thereby corroborating the theory of collective choice.A Multi-dimensional Model of Gridlock: We investigate the issue of the stability of the status quo in the basic model . Our model generalizes Kreshbiel's (1996, 1998) model of legislative gridlock and provides the following insight: in multi-dimensional settings, complete gridlock of the sort in Krehbiel's model is rare, although a partial type of gridlock is possible.Contemporaneous Bargaining: We extend our equilibrium existence result to a model of simultaneous bargaining with multiple groups. Applications include the study of federal systems of government, bicameral legislatures, decisions within separate firms, and decisions within separate national assemblies. Bargaining in Economic Environments: We capture bargaining in economic contexts, give decisionmakers endowments and property rights over them, and allow endowments to vary stochastically over time. We focus on equilibrium existence and core equivalence. Dynamic Collective Choice: We allow bargaining to continue after an agreement has been reached - the outcome of bargaining in one period becomes the status quo point for bargaining in the next. We attempt to overcome difficult technical problems in the analysis of equilibrium existence in models of "ongoing" collective choice. In Section 3, we propose to study repeated elections, and generalize Duggan (1997) by allowing for a multi-dimensional policy space and more general preferences. The model of elections is mathematically quite similar to our basic model of bargaining, and the techniques we have developed in our analysis of bargaining enable us to establish the existence of stationary electoral equilibria, to characterize them, and to clarify their connection to the core.