On the indices of zeros of Nash fields

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 correspondenc e onto the underlying space of games. This is important since it implies th at ibr a wide class of dynamics local stability propel ties of zeros are de termined by the geometry of the Nash correspondence, providing further link s between learning or evolutionary game theory, the theory of equilibrium r efinements, and the geometry of Nash equilibrium, The result extends beyond general n-player games e.g. to Walrasian equilibrium theory. Journal of Ec onomic Literature Classification Numbers: C63, C72, D50. (C) 2000 Academic Press.