The Primal Auction: a new design for multi-commodity double auctions (original) (raw)
Related papers
Truthful and Competitive Double Auctions
Lecture Notes in Computer Science, 2002
In this paper we consider the problem of designing a mechanism for double auctions where bidders each bid to buy or sell one unit of a single commodity. We assume that each bidder's utility value for the item is private to them and we focus on truthful mechanisms, ones where the bidders' optimal strategy is to bid their true utility. The profit of the auctioneer is the difference between the total payments from buyers and the total payments to the sellers. We aim to maximize this profit. We extend the competitive analysis framework of basic auctions [12] and give an upper bound on the profit of any truthful double auction. We then reduce the competitive double auction problem to basic auctions by showing that any competitive basic auction can be converted into a competitive double auction with a competitive ratio of twice that of the basic auction. In addition, we show that better competitive ratios can be obtained by directly adapting basic auction techniques to the double auction problem. In doing so, we generalize the consensus and revenue estimate technique from [11] to a wider class of problems.
Truthful Double Auction Mechanisms
Operations Research, 2008
Following the multistage design approach, we propose two asymptotically efficient truthful double auction mechanisms, the BC-LP mechanism and the MBC mechanism, for an exchange market with many buyers and sellers. In this market, each buyer wants to procure a bundle of commodities and each seller supplies one unit of a commodity. Furthermore, various transaction-related costs will be incurred when a buyer trades with a seller. We prove that under both mechanisms, truthful bidding is a dominant strategy for all buyers and sellers when the buyers' bundle information and the transaction cost information are common knowledge. The BC-LP mechanism can be implemented by just solving two linear programs, whereas the MBC mechanism has a higher complexity. The empirical study shows that the MBC mechanism achieves higher efficiency over the BC-LP mechanism and that both outperform the KSM-TR mechanism, the only known truthful mechanism for a more restrictive exchange market.
Instantiating the Contingent Bids Model of Truthful Interdependent Value Auctions
We consider the problem of auction design with agents that have interdependent values, i.e. values that depend on each others' private signals. We adopt the contingent bids model of Dasgupta and Maskin [3], and allow agents to submit bids of the form " if player 1 bids xforgoodthenIwillbidx for good then I will bid xforgoodthenIwillbidy. " Our main contribution is to identify a specific linear valuation model for which there exists an efficient auction for a single item, and then extend this to provide an approximately efficient combinatorial auction with single-minded bidders. In both auction, winners and payments are computed from the fixed point of the valuation mapping defined by contingent bids. We also adopt search in order to construct a variation on the single-item auction with improved revenue. In closing, we discuss the (many) challenges in moving to more general models of interdependent valuations.
Truth revelation in approximately efficient combinatorial auctions
1999
Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms -in particular, their truth revelation properties -assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that, for our restricted class of players, they imply that truthful strategies are dominant. Those properties have applicability beyond the specific auction studied.
Decomposing Truthful and Competitive Online Double Auctions
In this paper, we study online double auctions, where multiple sellers and multiple buyers arrive and depart dynamically to exchange one commodity. We show that there is no deterministic online double auction that is truthful and competitive for maximising social welfare in an adversarial model. However, given the prior information that sellers are patient and the demand is not more than the supply, a deterministic and truthful greedy mechanism is actually 2-competitive, i.e. it guarantees that the social welfare of its allocation is at least half of the optimal one achievable offline. Moreover, if the number of incoming buyers is predictable, we demonstrate that an online double auction can be reduced to an online one-sided auction, and the truthfulness and competitiveness of the reduced online double auction follow that of the online one-sided auction. Notably, by using the reduction, we find a truthful mechanism that is almost 1-competitive, when buyers arrive randomly. Finally, we argue that these mechanisms also have a promising applicability in more general settings without assuming that sellers are patient, by decomposing a market into multiple sub-markets.
Near Optimal Non-truthful Auctions
2011
In several e-commerce applications, non-truthful auctions have been preferred over truthful weakly dominant strategy ones partly because of their simplicity and scalability. Although non-truthful auctions can have weaker incentive constraints than truthful ones, the question of how much more revenue they can generate than truthful auctions is not well understood. We study this question for natural and broad classes of non-truthful mechanisms, including quasi-proportional sharing and weakly monotonic auctions. Quasi-proportional sharing mechanisms allocate to each bidder i an amount of resource proportional to a monotonic and concave function f (b i ) where b i is the bid of bidder i and ask for a payment of b i . Weakly monotonic auctions refer to a more general class of auctions which satisfy some natural continuity and monotonicity conditions.
Econometrica, 2002
An analogue of multi-unit auction is provided when bidders have interdependent values and one-dimensional private information. The analogue is strategically equivalent to a collection of two-bidder single-unit second-price auctions and it possesses an e¢cient ex-post equilibrium.
Implementing the Optimal Auction
2003
In a general framework with independent private values of the bidders, we propose a game, with a simple economic interpretation, that allows implementing the optimal auction outcome when the seller ignores the distributions of the different bidders' valuations. In this robust or detail-free implementation procedure, a second-price auction is organized and the winner volunteers a payment to the seller; this payment can then be challenged by another bidder who knows the distribution of the winner's valuation. Dans un cadre du modèle d'enchères avec des valeurs privées indépendantes, nous proposons un jeu, ayant une interprétation économique simple, qui permet de mettre en oeuvre les enchères optimales même quand le vendeur ignore les distributions des volontés à payer des différents soumissionnaires. Dans cette procédure robuste (detail-free), une enchère au deuxième prix est organisée et le gagnant de cette enchère propose un paiement au vendeur; ce paiement peut alors...
An Approximate Truthful Mechanism for Combinatorial Auctions with Single Parameter Agents
Internet Mathematics, 2004
Mechanism design seeks algorithms whose inputs are provided by selfish agents who would lie if it were to their advantage. Incentive-compatible mechanisms c o m p e lt h ea g e n t st ot e l lt h et r u t hb ym a k i n gi ti nt h e i rs e l f -i n t e r e s tt od os o . O ften, as in combinatorial auctions, such mechanisms involve the solution of NP-hard problems. Unfortunately, approximation algorithms typically destroy incentive compatibility. Randomized rounding is a commonly used technique for designing approximation algorithms. We devise a version of randomized rounding that is incentivecompatible, giving a truthful mechanism for combinatorial auctions with single parameter agents (e.g., "single minded bidders") that approximately maximizes the social value of the auction. We discuss two orthogonal notions of truthfulness for a randomized mechanism-truthfulness with high probability and in expectation-and give a mechanism that achieves both simultaneously.