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

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.

The difference between auction and negotiation mechanisms has blurred with the arrival of the Internet and electronic commerce. The new media provide new opportunities and mechanisms to cooperate or to compete, taking advantage of computer power, the communication possibilities of the network, and the fact that millions of people and businesses are online simultaneously. We discuss the characteristics of different types of auctions and negotiations. We extend the discussion to combinations and hybrids of auctions and negotiations and their possible roles in e-commerce. 1.

increasingly important aspect of e-commerce, both in the business to business and business to consumer domains. As a result of this, it is often possible to find many auctions selling similar goods on the web. However, when an individual is attempting to purchase such a good, they will usually bid in one, or a small number, of such auctions. This results in two forms of ine#ciency. Firstly, the individual may pay more for the good than would be expected in an ideal market. Secondly, some sellers may fail to make a sale that could take place in an ideal market.

Combinatorial exchanges arise naturally in multi-agent systems that execute hierarchically decomposed tasks, when the agents have uncertainty about each other's tasks and each other's capability of handling tasks. In a combinatorial exchange, the information is aggregated to one party who then decides the task allocation among the agents. Unfortunately, such exchanges can require that bidders calculate and communicate an exponential number of bids, each of which may involve solving a hard planning problem. We present a design for an auctioneer agent that can construct and clear a combinatorial exchange using preference elicitation. This design extends existing analyses of elicitation in the combinatorial auction to the combinatorial exchange. We also introduce the concept of item discovery that uses elicitation to construct the exchange when there is uncertainty about which items should be considered in the market. Our experimental results, in a multi-robot exploration domain, show that elicitation significantly reduces the number of bids that must be evaluated in order to clear the market. More important, the proportion of bids that must be evaluated decreases as we scale to larger problem instances. We also present experimental results for an anytime version of the elicitation algorithm.

Combinatorial auctions provide a valuable mechanism for the allocation of goods in settings where buyer valuations exhibit complex structure with respect to substitutability and complementarity. Most algorithms are designed to work with explicit "flat" bids for concrete bundles of goods. However, logical bidding languages allow the expression of complex utility functions in a natural and concise way, and have recently attracted considerable attention.

Combinatorial auctions where agents can bid on bundles of items are desirable because they allow the agents to express complementarity and substitutability between the items. However, expressing one's preferences can require bidding on all bundles. Selective incremental preference elicitation by the auctioneer was recently proposed to address this problem [4], but the idea was not evaluated. In this paper we show, experimentally and theoretically, that automated elicitation provides a drastic benefit. In all of the elicitation schemes under study, as the number of items for sale increases, the amount of information elicited is a vanishing fraction of the information collected in traditional "direct revelation mechanisms" where bidders reveal all their valuation information. Most of the elicitation schemes also maintain the benefit as the number of agents increases. We develop more effective elicitation policies for existing query types. We also present a new query type that takes the incremental nature of elicitation to a new level by allowing agents to give approximate answers that are refined only on an as-needed basis. In the process, we present methods for evaluating different types of elicitation policies.

Matchmaking is the process of mediating demand and supply based on profile information. Matchmaking plays a crucial role in agent-based electronic marketplaces: the problem to be solved is to find the most appropriate agents, products, or services for a task, negotiation, or market transaction. Most real-world problems require multidimensional matchmaking, i.e., the ability to combine various dimensions of decision-making to define an overall solution to a matchmaking problem, requiring the interplay of multiple matchmaking algorithms. In addition, in order to be applicable for real-world applications, the matchmaking component must be easily integrated into standard industrial marketplace platforms. The work described in this work aims at deploying agent-based matchmaking for industrial electronic business applications. The main contributions of this work are the following: (i) we provide a configurable framework called GRAPPA (Generic Request Architecture for Passive Provider Agents) which is designed to be adapted to electronic marketplace applications. Using GRAPPA, system designers can easily specify demand and supply profiles as XML objects; (ii) within GRAPPA we provide an extensible library of matchmaking functions (building blocks) that can be used for rapid development of matchmaking solutions that include standard information retrieval algorithms. Areas: artificial market systems and electronic commerce, middle agents, agent-based software engineering

This paper is a contribution towards the body of literature which views negotiation in a qualitative light. It builds on an existing logical framework for negotiation between rational, cooperative, truthful agents proposed in (Meyer, Kwok, & Zhang 2003). We show that agents equipped with negotiation strategies corresponding to basic AGM belief revision operations are capable of reaching exactly the permissible deals defined and discussed in (Meyer, Kwok, & Zhang 2003). Each agent has to present a set of weakened demands to the other party who, in return, is obliged to accept all weakened demands. The acceptance of demands is modelled by basic AGM belief revision. We extend the logical framework of (Meyer, Kwok, & Zhang 2003) by considering scenarios in which the initial demand sets of agents may vary. We show that it forces agents to limit their negotiation strategies to AGM belief revision satisfying the supplementary AGM postulates. This leads to the redefinition of a negotiation strategy as a preference relation on demands. This extended framework provides a description of the deals that an agent ought to consider as reasonable, but provides no information on how it should go about choosing a particular deal. We conclude with suggestions on how negotiation strategies can be used to do so.