2012/02/29 by Georgios Piliouras, Piliouras, Georgios, Tomáš Valla +3
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Game Theory and Applications #Game Theory and Voting Systems
paper · doi:10.48550/arxiv.1203.0050
openalex publication_date 2012/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3].