Group-Strategyproof Mechanisms for Network Design Games via Primal-Dual Algorithms

About 15 years ago, Goemans and Williamson formally introduced the primal-dual framework for approximation algorithms and applied it to a class of network design optimization problems. Since then literally hundreds of results appeared that extended, modified and applied the technique to a wide range of optimization problems. In this paper we define a class of cost-sharing games arising from Goemans and Williamson’s original network design problems. We then show how to derive a groupstrategyproof (i.e., collusion resistant) mechanism for such a game, using an existing primal-dual algorithm for the underlying optimization problem as a black box. The budgetbalance factor of this mechanism is proportional to the performance ratio of the primal-dual algorithm if the optimization problem satisfies an additional technical condition. Most existing collusion-resistant cost-sharing mechanisms are obtained through skillful adaptation of existing primal-dual algorithms for the associated optimization problems. This paper shows that, at least for a large class of games arising from network design problems, no such adaptation is necessary.