Noncooperative game theory provides a normative framework for analyzing strategic interactions.

significant attention in single-agent settings. It is also a key problem in multiagent systems, but has received little attention here so far. In this setting, the agents may have different preferences that often must be aggregated using voting.

We consider auction design in a setting with costly preference elicitation. We motivate the role of proxy agents, that are situated between bidders and the auction, and maintain partial information about agent preferences and compute equilibrium bidding strategies based on the available information. The proxy agents can also elicit additional preference information incrementally during an auction. We show that indirect mechanisms, such as proxied ascending-price auctions, can achieve better allocative efficiency with less preference elicitation than direct mechanisms, such as sealed-bid auctions.

In this paper we explore the relationship between "preference elicitation", a learning-style problem that arises in combinatorial auctions, and the problem of learning via queries studied in computational learning theory. Preference elicitation is the process of asking questions about the preferences of bidders so as to best divide some set of goods. As a learning problem, it can be thought of as a setting in which there are multiple target concepts that can each be queried separately, but where the goal is not so much to learn each concept as it is to produce an "optimal example". In this work, we prove a number of similarities and differences between two-bidder preference elicitation and query learning, giving both separation results and proving some connections between these problems.

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.

The revelation principle is a cornerstone tool in mechanism design. It states that one can restrict attention, without loss in the designer's objective, to mechanisms in which A) the agents report their types completely in a single step up front, and B) the agents are motivated to be truthful. We show that reasonable constraints on computation and communication can invalidate the revelation principle. Regarding A, we show that by moving to multi-step mechanisms, one can reduce exponential communication and computation to linear---thereby answering a recognized important open question in mechanism design. Regarding B, we criticize the focus on truthful mechanisms---a dogma that has, to our knowledge, never been criticized before. First, we study settings where the optimal truthful mechanism is -complete to execute for the center. In that setting we show that by moving to insincere mechanisms, one can shift the burden of having to solve the -complete problem from the center to one of the agents. Second, we study a new oracle model that captures the setting where utility values can be hard to compute even when all the pertinent information is available---a situation that occurs in many practical applications. In this model we show that by moving to insincere mechanisms, one can shift the burden of having to ask the oracle an exponential number of costly queries from the center to one of the agents. In both cases the insincere mechanism is equally good as the optimal truthful mechanism in the presence of unlimited computation. More interestingly, whereas being unable to carry out either difficult task would have hurt the center in achieving his objective in the truthful setting, if the agent is unable to carry out either difficult task, the value of the center's objec...

Combinatorial auctions allow bidders to express complex valuations on bundles of items, and have been proposed in settings as diverse as the allocation of floor space in a new condominium building to individual units (Wired 2000) and the allocation of take-off and landing slots at airports (Smith, Forward). Many applications are described in Part V of this book. The promise of combinatorial auctions (CAs) is that they can allow bidders to better express their private information about preferences for different outcomes and thus enhance competition and market efficiency. Much effort has been spent on developing algorithms for the hard problem of winner determination once bids have been received (Sandholm, Chapter 14). Yet, preference elicitation has emerged as perhaps the key bottleneck in the real-world deployment of combinatorial auctions. Advanced clearing algorithms are worthless if one cannot simplify the bidding problem facing bidders. Preference elicitation is a p

Preference elicitation --- the process of asking queries to determine parties' preferences --- is a key part of many problems in electronic commerce. For example, a shopping agent needs to know a user's preferences in order to correctly act on her behalf, and preference elicitation can help an auctioneer in a combinatorial auction determine how to best allocate a given set of items to a given set of bidders. Unfortunately, in the worst case, preference elicitation can require an exponential number of queries even to determine an approximately optimal allocation. In this paper we study natural special cases of preferences for which elicitation can be done in polynomial time via value queries. The cases we consider all have the property that the preferences (or approximations to them) can be described in a polynomial number of bits, but the issue here is whether they can be elicited using the natural (limited) language of value queries. We make a connection to computational learning theory where the similar problem of exact learning with membership queries has a long history. In particular, we consider preferences that can be written as read-once formulas over a set of gates motivated by a shopping application, as well as a class of preferences we call Toolbox DNF, motivated by a type of combinatorial auction. We show that in each case, preference elicitation can be done in polynomial time. We also consider the computational problem of allocating items given the parties' preferences, and show that in certain cases it can be done in polynomial time and in other cases it is NP-complete. Given two bidders with Toolbox-DNF preferences, we show that allocation can be solved via network flow. If parties have read-once formula preferences, then allocation is NP-hard even with ju...

Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of partial orders and a candidate c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We prove that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NP-complete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NP-complete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNP-complete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomial-time algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.

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.