One of the major achievements of mechanism design theory is the family of truthful (incentive compatible) mechanisms often called VCG (named after Vickrey, Clarke and Groves). When applying VCG mechanisms to complex mechanism design problems such as combinatorial auctions a problem emerges: even finding optimal outcomes is computationally intractable. A striking observation is that if the optimal outcome is replaced by the results of computationally tractable approximation algorithms or heuristics then the resulting mechanism (termed VCG-based) is no longer necessarily truthful! The first part of this paper considers this problem in depth and shows that it is almost universal. Specifically, we prove that essentially all reasonable approximations or heuristics for combinatorial auctions as well as a wide class of cost minimization problems yield non-truthful VCG-based mechanisms. The second part of this paper proposes a method for handling this non-truthfulness. We introduce a...

Combinatorial auctions where bidders can bid on bundles of items can lead to more economical allocations, but determining the winners is-complete and inapproximable. We present CABOB, a sophisticated search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid ordering heuristics, and a host of structural observations. Experiments against CPLEX 7.0 show that CABOB is usually faster, never drastically slower, and in many cases drastically faster. We also uncover interesting aspects of the problem itself. First, the problems with short bids that were hard for the first-generation of specialized algorithms are easy. Second, almost all of the CATS distributions are easy, and become easier with more bids. Third, we test a number of random restart strategies, and show that they do not help on this problem because the run-time distribution does not have a heavy tail (at least not for CABOB). 1

This paper presents eMediator, an electronic commerce server prototype that demonstrates ways in which algorithmic support and game-theoretic incentive engineering can jointly improve the efficiency of ecommerce. eAuctionHouse, the configurable auction server, includes a variety of generalized combinatorial auctions and exchanges, pricing schemes, bidding languages, mobile agents, and user support for choosing an auction type. We introduce two new logical bidding languages for combinatorial markets: the XOR bidding language and the OR-of-XORs bidding language. Unlike the traditional OR bidding language, these are fully expressive. They therefore enable the use of the Clarke-Groves pricing mechanism for motivating the bidders to bid truthfully. eAuctionHouse also supports supply/demand curve bidding. eCommitter, the leveled commitment contract optimizer, determines the optimal contract price and decommitting penalties for a variety of leveled commitment contracting mechanisms, taking into account that rational agents will decommit strategically in Nash equilibrium. It also determines the optimal decommitting strategies for any given leveled commitment contract. eExchangeHouse, the safe exchange planner, enables unenforced anonymous exchanges by dividing the exchange into chunks and sequencing those chunks to be delivered safely in alternation between the buyer and the seller.

Generalized Vickrey mechanisms have received wide attention in the literature because they are efficient and strategyproof, i.e. truthful bidding is optimal whatever the bids of other agents. However it is well-known that it is impossible for an exchange, with multiple buyers and sellers, to be efficient and budget-balanced, even putting strategy-proofness to one side. A market-maker in an efficient exchange must make more payments than it collects. We enforce budget-balance as a hard constraint, and explore payment rules to distribute surplus after an exchange clears to minimize distance to Vickrey payments. Different rules lead to different levels of truthrevelation and efficiency. Experimental and theoretical analysis suggest a simple Threshold scheme, which gives surplus to agents with payments further than a certain threshold value from their Vickrey payments. The scheme appears able to exploit agent uncertainty about bids from other agents to reduce manipulation and boost allocative efficiency in comparison with other simple rules.

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NP-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster—especially in cases with structure. CABOB’s search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem—the run-time distribution does not have a heavy tail.

In most real-world (electronic) marketplaces, there are other considerations besides maximizing immediate economic value. We present a sound way of taking such considerations into account via side constraints and non-price attributes. Side constraints have a significant impact on the complexity of market clearing. Budget constraints, a limit on the number of winners, and XOR-constraints make even noncombinatorial markets-complete to clear. The latter two make markets-complete to clear even if bids can be accepted partially. This is surprising since, as we show, even combinatorial markets with a host of very similar side constraints can be cleared in polytime. An extreme equality constraint makes combinatorial markets polytime clearable even if bids have to be accepted entirely or not at all. Finally, we present a way to take into account additional attributes using a bid re-weighting scheme, and prove that it does not change the complexity of clearing. All of the results hold for auctions as well as exchanges, with and without free disposal. 1

: We give an approach to automating the negotiation of business contracts. Our goal is to develop a language for both (1.) fully-specified, executable contracts and (2.) partially-specified contracts that are in the midst of being negotiated, including via automated auctions. Our starting point for this language is Courteous Logic Programs (CLP's), a form of logic-based knowledge representation (KR) that is semantically declarative, intuitively natural, computationally tractable, and practically executable. A CLP is suitable in particular to represent a fully-specified executable contract. The basic CLP KR also facilitates modification during negotiation, because it includes prioritized conflict handling features that facilitate modification. Beyond the basic CLP KR, we have developed an initial ontology, and an associated style of representation, to specify additional aspects of a partial contract and of a negotiation process. The initial ontology specifies the set of negotiables and ...

We are interested in supporting multi-agent contracting, in which customer agents solicit the resources and capabilities of other, self-interested agents in order to accomplish their goals. Goals may

In this paper we study the problem of online market clearing where there is one commodity in the market being bought and sold by multiple buyers and sellers whose bids arrive and expire at different times. The auctioneer is faced with an online clearing problem of deciding which buy and sell bids to match without knowing what bids will arrive in the future. For maximizing profit, we present a (randomized) online algorithm with a competitive ratio of ln(p max min )+1, when bids are in a range [p min ,p max ], which we show is the best possible. A simpler algorithm has a ratio twice this, and can be used even if expiration times are not known. For maximizing the number of trades, we present a simple greedy algorithm that achieves a factor of 2 competitive ratio if no money-losing trades are allowed. Interestingly, we show that if the online algorithm is allowed to subsidize matches --- match money-losing pairs if it has already collected enough money from previous pairs to pay for them --- then it can be 1-competitive with respect to the optimal offline algorithm that is not allowed subsidy. That is, the ability to subsidize is at least as valuable as knowing the future. We also consider the objectives of maximizing buy or sell volume, and present algorithms that achieve a competitive ratio of 2(ln(p max /p min ) + 1), or ln(p max /p min ) + 1 if the online algorithm is allowed subsidization. We show the latter is the best possible competitive ratio for this setting. For social welfare maximization we also obtain an optimal competitive ratio, which is below ln(p max /p min ). We present all of these results as corollaries of theorems on online matching in an incomplete interval graph.

Recent algorithms provide powerful solutions to the problem of determining cost-minimizing (or revenue-maximizing) allocations of items in combinatorial auctions. However, in many settings, criteria other than cost (e.g., the number of winners, the delivery date of items, etc.) are also relevant in judging the quality of an allocation. Furthermore, the bid taker is usually uncertain about her preferences regarding tradeoffs between cost and nonprice features. We describe new methods that allow the bid taker to determine (approximately) optimal allocations despite this. These methods rely on the notion of minimax regret to guide the elicitation of preferences from the bid taker and to measure the quality of an allocation in the presence of utility function uncertainty. Computational experiments demonstrate the practicality of minimax computation and the efficacy of our elicitation techniques.