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.

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. e markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents' valuations of the items, but not the actual valuations; thus the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism, and the best social welfare possible.Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a se ing where buyers have XOS valuations and sellers' valuations are additive.is is the rst such approximation mechanism for a two-sided market se ing where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain "unnatural" transactions satis ed by SBB. We show that the stronger version is satis ed by our mechanisms.

Bilateral trade is a fundamental economic scenario comprising a strategically acting buyer and seller (holding an item), each holding valuations for the item, drawn from publicly known distributions. A mechanism is supposed to facilitate trade between these agents, if such trade is beneficial. It was recently shown that the only mechanisms that are simultaneously dominant strategy incentive compatible, strongly budget balanced, and ex-post individually rational, are fixed price mechanisms, i.e., mechanisms that are parametrised by a price p, and trade occurs if and only if the valuation of the buyer is at least p and the valuation of the seller is at most p. The gain from trade is the increase in welfare that results from applying a mechanism; here we study the gain from trade achievable by fixed price mechanisms. We explore this question for both the bilateral trade setting, and a double auction setting where there are multiple buyers and sellers. We first identify a fixed price mechanism that achieves a gain from trade of at least 2/r times the optimum, where r is the probability that the seller's valuation does not exceed the buyer's valuation. This extends a previous result by McAfee. Subsequently, we improve this approximation factor in an asymptotic sense, by showing that a more sophisticated rule for setting the fixed price results in an expected gain from trade within a factor O(log(1/r)) of the optimal gain from trade. This is asymptotically the best approximation factor possible. Lastly, we extend our study of fixed price mechanisms to the double auction setting defined by a set of multiple i.i.d. unit demand buyers, and i.i.d. unit supply sellers. We present a fixed price mechanism that achieves a gain from trade that achieves for all ǫ > 0 a gain from trade of at least (1 − ǫ) times the expected optimal gain from trade with probability 1 − 2/e #T ǫ 2 /2 , where #T is the expected number of trades resulting from the double auction. This can be interpreted as a "large market" result: Full efficiency is achieved in the limit, as the market gets thicker.

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...

We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is query complexity, that is, how many queries are necessary or sufficient to compute an exact or approximate Nash equilibrium. We show that exact equilibria cannot be found via query-efficient algorithms. We also give an example of a 2-strategy, 3-player anonymous game that does not have any exact Nash equilibrium in rational numbers. However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria. We investigate four sub-classes of anonymous games previously considered by [5, 15]. Our main result is a new randomized query-efficient algorithm that finds a O(n −1/4)-approximate Nash equilibrium querying˜Oquerying˜ querying˜O(n 3/2) payoffs and runs in time˜Otime˜ time˜O(n 3/2). This improves on the running time of pre-existing algorithms for approximate equilibria of anonymous games, and is the first one to obtain an inverse polynomial approximation in poly-time. We also show how this can be utilized as an efficient polynomial-time approximation scheme (PTAS). Furthermore, we prove that Ω(n log n) payoffs must be queried in order to find any ǫ-well-supported Nash equilibrium, even by randomized algorithms.