Approximately-strategyproof and tractable multiunit auctions

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multiunit allocation problem. The bidding language allows marginal-decreasing piecewise-constant curves and quantity-based side constraints. We develop a fully polynomial-time approximation scheme for the multiunit allocation problem, which computes a (1+e) approximation in worst-case time T=O(n³/e), given n bids each with a constant number of pieces. We integrate this approximation scheme within a Vickrey–Clarke–Groves mechanism and compute payments for an asymptotic cost of O(Tlogn). The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by eV/(1+e), where V is the total surplus in the efficient outcome.