Algorithms as mechanisms: the price of anarchy of relax-and-round

We show that algorithms that follow the relax-and-round paradigm translate approximation guarantees into Price of Anarchy guarantees, provided that the rounding is oblivious and the relaxation is smooth. We use this meta result to obtain simple, near-optimal mechanisms for a broad range of optimization problems such as combinatorial auctions, the maximum traveling salesman problem, and packing integer programs. In each case the resulting mechanism matches or beats the performance guarantees of known mechanisms.