On the Price of Truthfulness in Path Auctions

We study the frugality ratio of truthful mechanisms in path auctions, which measures the extent to which truthful mechanisms “overpay” compared to non-truthful mechanisms. In particular we consider the fundamental case that the graph is composed of two node-disjoint s-t-paths of length s1 and s2 respectively, and prove an optimal √ s1s2 lower bound (an improvement over √ s1s2/2). This implies that the √ mechanism of Karlin et al. for path auctions is 2-competitive (an improvement over 2 √ 2), and is optimal if the graph is a series-parallel network. Moreover, our results extend to universally truthful randomized mechanisms as well.