Axiomatic Study of Solutions

这个项目是数学家们雄心勃勃的努力的一部分。 经济学家要确定并严格研究基本的 个人和集体选择的原则。 这些 原则，当应用于具体问题时，采取以下形式： 公理，并已被证明在提供新的 对解决经济问题的见解， 统一了经济理论的各个领域。 该项目研究和表征满足以下条件的解决方案： 增广原则及其“对偶”、一致性 原则 一致性是指无论结果如何 任何一个子问题，其中子问题大致意味着一个问题， 通过单独考虑一个子集， 代理商和他们的资源，从原来的问题。 增强的工作原理是相反的：任何问题的解决方案 应该与解决更大的问题相一致， 其中给定的问题是一个子问题。 这些原则 适用于以下几类经济问题： 谈判，破产与税收，成本分摊，资源 在有公共神的经济体中分配。 这条基础研究路线很重要，因为它帮助我们 理解社会的组合之间的界限 哪些目标是可行的，哪些是不可行的。 比如说 项目确定了林达尔通信，其中一个 公共产品经济中分配的主要理论工具， 满足社会选择的基本原则， 精确的工具来量化给定的 通信不符合特定的要求。

This project is part of an ambitious effort by mathematical economists to identify and rigorously study fundamental principles of individual and collective choice. These principles, when applied to specific problems, take the form of axioms and have proved extremely powerful in providing new insights into the solutions to economic problems and in unifying the varied areas of economic theory. This project studies and characterizes solutions satisfying the augmentation principle an its "dual", the consistency principle. Consistency is the property that whatever outcome of any subproblem where subproblem roughly means a problem derived from the original by considering separately a subset of the agents, and their resources, from the original problem. Augmentation works in reverse: any solution to a problem should be consistent with the solution to a larger problem of which the given problem is a subproblem. The principles are applied to the following classes of economic problems: bargaining, bankruptcy and taxation, cost allocation, resource allocation in economies with public godds. This line of basic research is important because it helps us understand the boundary between which combinations of social objectives are feasible and which are not. For example, the project determines when the Lindahl correspondence, one of the main theoretical tools for allocation in public good economies, satisfies fundamental principles of social choice and develops precise tools for quantifying the extent to which a given correspondence fails to meet a given requirement.