On the indices of zeros of Nash fields

• 成果类型: Article
• 署名作者: DeMichelis, S; Germano, F
• 署名单位: University of Pavia; Tel Aviv University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2000.2669
• 发表日期: 2000
• 页码: 192-217
• 关键词: degree; DYNAMICS; STABILITY; geometry of equilibrium correspondences

摘要

We show a fundamental property of dynamics whose zeros are essentially the Nash equilibria of underlying games. namely. the indices of zeros coincide with the degrees of the projection from the graph of the Nash correspondence onto the underlying space of games. This is important since it implies that ibr a wide class of dynamics local stability propel ties of zeros are determined by the geometry of the Nash correspondence, providing further links between learning or evolutionary game theory, the theory of equilibrium refinements, and the geometry of Nash equilibrium, The result extends beyond general n-player games e.g. to Walrasian equilibrium theory. Journal of Economic Literature Classification Numbers: C63, C72, D50. (C) 2000 Academic Press.