Approximately Efficient Two-Sided Combinatorial Auctions

Abstract

One-sided markets have been studied in economics for several decades and more recently in computer science. Mechanism Design in one-sided markets aims to find an efficient (high-welfare) allocation of a set of items to a set of agents, while ensuring that truthfully reporting the input data is the best strategy for the agents. The cornerstone method in mechanism design is the Vickrey-Clarke-Groves (VCG) mechanism [22,4,12] that optimizes the social welfare of the agents while providing the right incentives for truth-telling: VCG mechanisms are dominant strategy incentive compatible (DSIC), and in many mechanism design settings, VCG is also individually rational (IR). IR requires that participating in the mechanism is beneficial to each agent. DSIC requires that truthfully reporting one's preferences to the mechanism is a dominant strategy for each agent, independently of what the other agents report.Recently, increased attention has been on the problems that arise in two-sided markets, in which the set of agents is partitioned into buyers and sellers. As opposed to the one-sided setting (where one could say that the mechanism itself initially holds the items), in the two-sided setting the items are initially held by the set of sellers, who express valuations over the items they hold, and who are assumed to act rationally and strategically. The mechanism's task is now to decide which buyers and sellers should trade, and at which prices. There is a growing interest in two-sided markets that can be attributed to various important applications. Examples range from selling display-ads on ad exchange platforms, the US FCC spectrum license reallocation, and stock exchanges. Twosided markets are usually studied in a Bayesian setting: there is public knowledge of probability distributions, one for each buyer and one for each seller, from which the valuations of the buyers and sellers are drawn.In two-sided markets, a further important requirement is strong budget-balance (SBB), which states that monetary transfers happen only among the agents in the market, i.e., the buyers and the sellers are allowed to trade without leaving to the mechanism any share of the payments, and without the mechanism adding money into the market. A weaker version of SBB often considered in the literature is weak budget-balance (WBB), which only requires the mechanism not to inject money into the market.Unfortunately, Myerson and Satterthwaite [16] proved that it is impossible for an IR, Bayesian incentive compatible (BIC), 6 and WBB mechanism to maximize social welfare in such a market, even in the bilateral trade setting, i.e., when there is just one seller and one buyer. 7 Despite the numerous above mentioned practical contexts that need the application of combinatorial two-sided market mechanisms, we are not aware of any mechanism that approximates the social welfare while meeting the IR, IC and SBB requirements. The purpose of this paper is to provide mechanisms that satisfy these requirements and achieve an O(1)-approximation to the social...

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