On the Computational Complexity of Mechanism Design in Single-Crossing Settings

We explore the performance of polynomial-time incentive-compatible mechanisms in single-crossing domains. Single-crossing domains were extensively studied in the economics literature. Roughly speaking, a domain is single crossing if monotonicity characterizes incentive compatibility (intuitively, an algorithm is monotone if a bidder that "improves"his valuation is allocated a better outcome). That is, single-crossing domains are the standard mathematical formulation of domains that are informally known as "single parameter". In all major single-crossing domains studied so far (e.g., welfare maximization in various auctions with single-minded bidders, makespan minimization on related machines), the performance of the best polynomial-time incentive-compatible mechanisms matches the performance of the best polynomial-time non-incentive-compatible algorithms.