Localization of the degree on lower-dimensional sets

  title={Localization of the degree on lower-dimensional sets},
  author={Jean-François Mertens},
  journal={International Journal of Game Theory},
  • J. Mertens
  • Published 1 June 2004
  • Mathematics
  • International Journal of Game Theory
Abstract.The restriction of an essential mapping to the inverse image of a simplex of arbitrary dimension is still essential. 
4 Citations

Some preliminary remarks on the relevance of topological essentiality in general equilibrium theory and game theory

We define an algebro-topological concept of essential map and we use it to prove several results in the theory of general equilibrium and nash equilibrium refinement.

Stable Outcomes of Generic Games in Extensive Form

We apply Mertens' dedinition of stability for a game in strategic form to a game in extensive form with perfect recall. We prove that if payoffs are generic then the outcomes of stable sets of

From evolutionary to strategic stability


Every game theorist knows of Mertens and Zamir (1985)'s universal beliefs space, which gives deep foundations to Harsanyi's model of Bayesian games, and Kohlberg and Mertens (1986)'s strategic



Algebraic Topology

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.


If two polyhedrons are locally subanalytically homeomorphic (that is, the graph is locally subanalytic), they are PL homeomorphic. A lo- cally subanalytic manifold is one whose coordinate

Stable Equilibria - A Reformulation. Part II. Discussion of the Definition, and Further Results

An equivalent definition that gets rid of the need to use Hausdorff limits is provided, and a "decomposition axiom" eliminates most of the algebraic possibilities, leaving only the "p-stable" sets, for p zero or prime.

Essential Maps and Manifolds

Let (M, partial derivative M) be a compact n-manifold with boundary, orientable over a field K with characteristic q . For f : (Y, partial derivative Y) --> (M, partial derivative M) , with Y

Introduction to Piecewise-Linear Topology

1. Polyhedra and P.L. Maps.- Basic Notation.- Joins and Cones.- Polyhedra.- Piecewise-Linear Maps.- The Standard Mistake.- P. L. Embeddings.- Manifolds.- Balls and Spheres.- The Poincare Conjecture

Lectures on Algebraic Topology

I Preliminaries on Categories, Abelian Groups, and Homotopy.- x1 Categories and Functors.- x2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups).- x3 Homotopy.- II Homology of Complexes.-

Stable Equilibria - A Reformulation: Part I. Definition and Basic Properties

A reformulation of stable equilibria is given, yielding a number of additional properties like backwards induction while still giving “typically,” i.e., except in “made up” examples, the same

From evolutionary to strategic stability