Optimal Budget-Feasible Mechanisms for Additive Valuations

In this paper, we obtain the tight approximation guarantees for budget-feasible mechanisms with an additive buyer. We propose a new simple randomized mechanism with an approximation ratio of $2$, improving the previous best known result of $3$. Our bound is tight with respect to either the optimal offline benchmark or its fractional relaxation. We also present a simple deterministic mechanism with the tight approximation guarantee of $3$ against the fractional optimum, improving the best known result of $(\sqrt2 + 2)$ against the weaker integral benchmark.