'Fixed points': extending and deepening our understanding of mathematical and computational aspects of game theory

这项工作将扩展和加深我们对博弈论的数学和计算方面的理解。 它将产生体现解决非线性方程组的新方法的计算机代码，这在经济学、化学等其他学科的应用研究的许多领域以及潜在的商业运作分析中是有用的。 该项目还将加深我们对这些系统的基本数学以及经济研究的其他数学基础的理解。 一个应用将是对投票规则所产生的相对权力的新衡量。 这些措施有助于民主制度的设计，使设计者能够评估它们产生的结果的公平性。

This work will extend and deepen our understanding of mathematical and computational aspects of game theory. It will produce computer code embodying new methods of solving systems of nonlinear equations, which is useful in many areas of applied research in economics, in other disciplines such as chemistry, and potentially in the analysis of business operations. The project will also deepen our understanding of the underlying mathematics of such systems, and of other mathematical foundations of economic research. One application will be a new measure of the relative power resulting from voting rules. Such measures assist the design of democratic institutions by allowing the designer to assess the fairness of the outcomes they produce.