Truthful Mechanisms for Two-Sided Markets via Prophet Inequalities

TL;DR

This paper introduces new mechanisms for welfare maximization in two-sided markets, leveraging prophet inequalities to achieve constant-factor approximations while satisfying strategic and budget constraints.

Contribution

It develops novel prophet inequality-based mechanisms for two-sided markets, improving approximation ratios and handling complex constraints like matroids and knapsacks.

Findings

Achieves 1/3 and 1/2 approximation ratios for matroid double auctions.

Designs mechanisms that are strongly and weakly budget-balanced.

Extends techniques to combinatorial auctions with online arrivals.

Abstract

We design novel mechanisms for welfare-maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are designed based on a powerful correspondence between two-sided markets and prophet inequalities. They satisfy individual rationality, dominant-strategy incentive compatibility, budget-balance constraints and give constant-factor approximations to the optimal social welfare. We improve previous results in several settings: Our main focus is on matroid double auctions, where the set of buyers who obtain an item needs to be independent in a matroid. We construct two mechanisms, the first being a $1/3$-approximation of the optimal social welfare satisfying strong budget-balance and requiring the agents to trade in a customized order, the second being a $1/2$-approximation, weakly budget-balanced and able to deal with online arrival determined by an adversary. In addition, we construct constant-factor approximations in two-sided markets when buyers need to fulfill a knapsack constraint. Also, in combinatorial double auctions, where buyers have valuation functions over item bundles instead of being interested in only one item, using similar techniques, we design a mechanism which is a $1/2$-approximation of the optimal social welfare, strongly budget-balanced and can deal with online arrival of agents in an adversarial order.