Probabilistic Techniques in Algorithmic Game Theory

We consider applications of probabilistic techniques in the framework of algorithmic game theory. We focus on three distinct case studies: (i) The exploitation of the probabilistic method to demonstrate the existence of approximate Nash equilibria of logarithmic support sizes in bimatrix games; (ii) the analysis of the statistical conflict that mixed strategies cause in network congestion games; (iii) the effect of coalitions in the quality of congestion games on parallel links. Keywords. Game Theory, Atomic Congestion Games, Coalitions, Convergence to Equilibria, Price of Anarchy. 1 Preliminaries and Notation For any k ∈ N, let [k] ≡ {1, 2, . . . , k}. M ∈ Fm×n denotes a m × n matrix (denoted by capital letters) whose elements belong to set F. We call a pair (A, B) ∈ (F × F)m×n (ie, an m × n matrix whose elements are ordered pairs of values from F) a bimatrix. A k×1 matrix is also considered to be an k-vector. Vectors are denoted by bold small letters (eg, x). ei denot...

• Type: Conference
• Year: 2007
• Where: SAGA
• Authors: Spyros C. Kontogiannis, Paul G. Spirakis
• Keywords: Congestion Games, Game Theory, Matrix, SAGA 2007