We extend Kohlberg and Mertens' (1986) structure theorem concerning the Nash equilibrium correspondence to show that its graph is not only homeomorphic to the underlying space of games but that it is also unknotted. This is then shown to have some basic consequences for dynamics whose rest...

Given a compact connected component of zeros of a vector field, we give a necessary condition for its asymptotic stability in terms of its index and Euler characteristic.

In an example with two objects and four bidders, some of which have superadditive values, we characterize the equilibria of a simultaneous ascending auction and compare the revenue and efficiency generated with ones generated by the sequential, the one-shot simultaneous, and the...

Two basic properties concerning the dynamic behavior of competitive equilibria of exchange economies with complete markets are derived essentially from the fact that the Walras correspondence has no knots.

We introduce a procedure that uses basic topological characteristics of equilibrium correspondences of standard equilibrium concepts, to define broad equivalence classes of finite generic games in normal form. The proposed procedure is viewed as a potentially useful way of both organizing the...