Nash-Walras Equilibria Topological Views on Implementation Theory

Nash and Walras equilibria have been studied from the angle of differential topology, yielding comparable results about existence and topological structure of equilibrium sets. Following a presentation of such results we shall review results on the Nash implementation of Walrasian equilibria. The purpose of the exercise is twofold: to establish a refinement criterion among multiple Walrasian equilibria and to study mechanisms closer to real markets than the Walrasian tâtonnement. Following up on results relating the best-reply dynamics and the natural projection, our conclusion is that some adjustments on the economic model are likely needed for implementation to link the topological structure of Walrasian and Nash equilibria.