Approximately Efficient Double Auctions with Strong Budget Balance

Abstract

Mechanism design for one-sided markets is an area of extensive research in economics and, since more than a decade, in computer science as well. Two-sided markets, on the other hand, have not received the same attention despite the numerous applications to web advertisement, stock exchange, and frequency spectrum allocation. This work studies double auctions, in which unit-demand buyers and unit-supply sellers act strategically.An ideal goal in double auction design is to maximize the social welfare of buyers and sellers with individually rational (IR), incentive compatible (IC) and strongly budgetbalanced (SBB) mechanisms. The first two properties are standard. SBB requires that the payments charged to the buyers are entirely handed to the sellers. This property is crucial in all the contexts that do not allow the auctioneer retaining a share of buyers' payments or subsidizing the market.Unfortunately, this goal is known to be unachievable even for the special case of bilateral trade, where there is only one buyer and one seller. Therefore, in subsequent papers, meaningful trade-offs between these requirements have been investigated.Our main contribution is the first IR, IC and SBB mechanism that provides an O(1)-approximation to the optimal social welfare. This result holds for any number of buyers and sellers with arbitrary, independent distributions. Moreover, our result continues to hold when there is an additional matroid constraint on the sets of buyers who may get allocated an item. To prove our main result, we devise an extension of sequential posted price mechanisms to two-sided markets. In addition to this, we improve the best-known approximation bounds for the bilateral trade problem.

Approximately Efficient Two-Sided Combinatorial Auctions

“…Notice that with non-unit-supply sellers, a constant approximation was not previously known even in the context of WBB or standard SBB. 2 Furthermore, we note that our mechanisms not only work for a more general se ing than that of [5], but also improve the approximation ratio for double auctions from 16 to 6.…”

“…A rst feature all our mechanisms share to guarantee DSBB is being a generalised version of two-sided sequential posted price mechanisms (SPMs) [5] for double auctions to combinatorial two-sided markets. ese mechanisms assign xed, pre-computed prices to each item so that these prices are the only ones for which the items can be traded.…”

“…ey obtain IR, DSIC, WBB mechanisms with a good approximation of the social welfare, for knapsack, matching and matroid allocation constraints. More recently, Colini-Baldeschi et al [5] presented the rst double auction that satis es IR, DSIC, and SBB, and approximates the optimal (expected) social welfare up to a constant factor.…”

“…For an allocation (X ,Y ) ∈ A, we shall use the notation 7 For two agents, it is straightforward to come up with alternative mechanisms that have the desired properties. 8 We note that the double auctions given in [5] Session 9a: Auctions --Equilibrium EC'17, June 26-30, 2017, Cambridge, MA, USA 1 R. Colini-Baldeschi, P.W. Goldberg, B. de Keijzer, S. Leonardi, T. Roughgarden, and S. Turche a SW B , SW S to respectively denote the buyers' and the sellers' contribution to the social welfare, i.e.,…”

Multi-Unit Bilateral Trade

“…Moreover, in case trade happens, the buyer pays p to the seller. In this paper we characterise the set of DSIC, IR, and WBB mechanisms for multi-unit bilateral trade, and we thereby generalise the characterisation of [8].…”