Stackelberg Strategies for Network Design Games

Abstract

We consider the Network Design game introduced by Anshelevich et al. [1] in which n source-destination pairs must be connected by n respective players equally sharing the cost of the used links. By considering the classical social function corresponding to the total network cost, it is well known that the price of anarchy for this class of games may be as large as n. One approach for reducing this bound is that of resorting on the Stackelberg model in which for a subset of $\lfloor \alpha n \rfloor$ coordinated players, with 0 ≤ α ≤ 1, communication paths inducing better equilibria are fixed. In this paper we show the effectiveness of Stackelberg strategies by providing optimal and nearly optimal bounds on the performance achievable by such strategies. In particular, differently from previous works, we are also able to provide Stackelberg strategies computable in polynomial time and lowering the price of anarchy from n to $2 \left( \frac 1 \alpha + 1 \right)$. Most of the results are extended to the social function , in which the maximum player cost is considered.

This research was partially supported by the grant NRF-RF2009-08 “Algorithmic aspects of coalitional games” and by the PRIN 2008 research project COGENT (COmputational and GamE-theoretic aspects of uncoordinated NeTworks), funded by the Italian Ministry of University and Research.