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

“不动点”：扩展和加深我们对博弈论数学和计算方面的理解

• 批准号: DP0773324
• 负责人: Prof Andrew McLennan
• 金额: $ 47.23万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2007
• 资助国家: 澳大利亚
• 起止时间: 2007-03-02 至 2013-03-01
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0773324
• 关键词: Fixed; points; extending; deepening; our

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.

这项工作将扩展和加深我们对博弈论数学和计算方面的理解。 它将产生包含求解非线性方程组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营分析中都很有用。 该项目还将加深我们对此类系统的基础数学以及经济研究的其他数学基础的理解。 其中一项应用是对投票规则产生的相对权力进行新的衡量。 这些措施允许设计者评估其产生的结果的公平性，从而有助于民主制度的设计。