Approximations of Nash equilibria

Universality of Nash Equilibria

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...

Symmetric Nash equilibria

Extreme Nash Equilibria

We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel links, to control the routing of its own assigned traffic. In a Na...