Fixed points as Nash equilibria

On the Complexity of Nash Equilibria and Other Fixed Points

We reexamine what it means to compute Nash equilibria and, more generally, what it means to compute a fixed point of a given Brouwer function, and we investigate the complexity of the associated problems. Specifically, we study the complexity of the following problem: given a finite game, Γ, with 3 or more players, and given > 0, compute an approximation within of some (actual) Nash equilibrium...

Equilibria, Fixed Points, and Complexity Classes

Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language l...

Nash and Correlated Equilibria

In this document we will look at useful facts and definitions about Nash and correlated equilibria for two person games. More specifically we’ll give a brief definition of both equilibria, and then we’ll point out the relation between them. We will next introduce a numerical approach aimed at calculating Nash Equilibria of a symmetric game we wish to explore in CME 334. A motivation for this ap...

Coalitional Nash Equilibria

Let G be an N -player game in strategic form and C be a set of permissible coalition of players (exogenously given). A strategy profile σ is a coalitional-equilibrium if no permissible coalition in C has a unilateral deviation that profits to all its members. At the two extremes: when C contains only singleton players, σ reduces to a Nash equilibrium and when C consists on all coalitions of pla...

Universality of Nash Equilibria