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SAGA
2007
Springer

Probabilistic Techniques in Algorithmic Game Theory

11 years 11 months ago
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...
Spyros C. Kontogiannis, Paul G. Spirakis
Added 09 Jun 2010
Updated 09 Jun 2010
Type Conference
Year 2007
Where SAGA
Authors Spyros C. Kontogiannis, Paul G. Spirakis
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