Strategyproof and fair matching mechanism for ratio constraints

We introduce a new type of distributional constraints called ratio constraints, which explicitly specify the required balance among schools in two-sided matching. Since ratio constraints do not belong to the known well-behaved class of constraints called M-convex set, developing a fair and strategyproof mechanism that can handle them is challenging. We develop a novel mechanism called quota reduction deferred acceptance (QRDA), which repeatedly applies the standard DA by sequentially reducing artificially introduced maximum quotas. As well as being fair and strategyproof, QRDA always yields a weakly better matching for students compared to a baseline mechanism called artificial cap deferred acceptance (ACDA), which uses predetermined artificial maximum quotas. Finally, we experimentally show that, in terms of student welfare and nonwastefulness, QRDA outperforms ACDA and another fair and strategyproof mechanism called Extended Seat Deferred Acceptance (ESDA), in which ratio constraints are transformed into minimum and maximum quotas

Strategy-Proof and Non-Wasteful Multi-Unit Auction via Social Network

Auctions via social network, pioneered by Li et al. (2017), have been attracting considerable attention in the literature of mechanism design for auctions. However, no known mechanism has satisfied strategy-proofness, non-deficit, non-wastefulness, and individual rationality for the multi-unit unit-demand auction, except for some naive ones. In this paper, we first propose a mechanism that satisfies all the above properties. We then make a comprehensive comparison with two naive mechanisms, showing that the proposed mechanism dominates them in social surplus, seller's revenue, and incentive of buyers for truth-telling. We also analyze the characteristics of the social surplus and the revenue achieved by the proposed mechanism, including the constant approximability of the worst-case efficiency loss and the complexity of optimizing revenue from the seller's perspective