Universality of Nash Equilibria by Ruchira

Universality of Nash Equilibria

Finding All Nash Equilibria of a Finite Game Using Polynomial Algebra

The set of Nash equilibria of a finite game is the set of nonnegative solutions to a system of polynomial equations. In this survey article we describe how to construct certain special games and explain how to find all the complex roots of the corresponding polynomial systems, including all the Nash equilibria. We then explain how to find all the complex roots of the polynomial systems for arbi...

Computation of Nash equilibria in finite games: introduction to the symposium

This is a collection of ten invited articles on the computation of Nash equilibria in finite games. Three (by Ruchira Datta, Jean-Jacques Herings and Ronald Peeters, and Tim Roughgarden) are longer surveys, the others present new research. All contributions attempt to make the material accessible and interesting to the non-specialist. The collection reflects in equal measure the state of resear...

Stability of Weakly Pareto-Nash Equilibria and Pareto-Nash Equilibria for Multiobjective Population Games

Using the method of generic continuity of set-valued mappings, this paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibria for multiobjective population games, when payoff functions are perturbed. More precisely, the paper investigates the continuity properties of the set of weakly Pareto-Nash equilibria and that of the set of Pareto-Nash equilibria under sufficiently smal...

A partial proof of Nash's Theorem via exchangeable equilibria

We give a novel proof of the existence of Nash equilibria in all finite games without using fixed point theorems or path following arguments. Our approach relies on a new notion intermediate between Nash and correlated equilibria called exchangeable equilibria, which are correlated equilibria with certain symmetry and factorization properties. We prove these exist by a duality argument, using H...