c ○ Xin Jiang, 2011itriou and Roughgarden described a polynomial-time algorithm (”Ellipsoid Against Hope”) for computing sample correlated equilibria of compactlyrepresented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to find an exact correlated equilibrium. We present a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomialtime identification of exact correlated equilibrium. Efficient computation of optimal correlated equilibria. We show that the polynomialtime solvability of what we call the deviation-adjusted social welfare problem is a sufficient condition for the tractability of the optimal correlated equilibrium problem. iii Preface Certain chapters of this thesis are based on publications (or submissions to publications) by my collaborators and me (under the name Albert Xin Jiang). Per requirement of UBC Faculty of Graduate Studies, I describe here the relative contributions of all collaborators. Chapter 3 is based on the article Action-Graph Games by Albert Xin Jiang, Kevin Leyton-Brown and Navin Bhat, published in Games and Economic Behavior,