Covering Games: Approximation through Non-cooperation

We propose approximation algorithms under game-theoretic considerations. We indroduce and study the general covering problem which is a natural generalization of the well-studied max-n-cover problem. In the general covering problem, we are given a universal set of weighted elements E and n collections of subsets of the elements. The task is to choose one subset from each collection such that the total weight of their union is as large as possible. In our game-theoretic setting, the choice in each collection is made by an independent player. For covering an element, the players receive a payoff defined by a nonincreasing utility sharing function. This function defines the fraction that each covering player receives from the weight of the elements. We show how to construct a utility sharing function such that every Nash Equilibrium approximates the optimal solution by a factor of 1 − 1 e . We also prove that any sequence of unilateral improving steps is polynomially bounded. This gi...

• Type: Conference
• Year: 2009
• Where: WINE
• Authors: Martin Gairing
• Keywords: Approximation Algorithm, Economy, General Covering Problem, Utility Sharing Function, WINE 2009