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109
Complexity Results about Nash Equilibria
, 2002
"... Noncooperative game theory provides a normative framework for analyzing strategic interactions. ..."
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Cited by 139 (11 self)
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Noncooperative game theory provides a normative framework for analyzing strategic interactions.
Vote Elicitation: Complexity and StrategyProofness
, 2002
"... significant attention in singleagent 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. ..."
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Cited by 87 (23 self)
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significant attention in singleagent 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.
Auction Design with Costly Preference Elicitation
 Annals of Mathematics and Artificial Intelligence
, 2003
"... 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. ..."
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Cited by 60 (10 self)
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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 ascendingprice auctions, can achieve better allocative efficiency with less preference elicitation than direct mechanisms, such as sealedbid auctions.
Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders
"... 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 part ..."
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Cited by 58 (13 self)
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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 NPcomplete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NPcomplete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNPcomplete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomialtime algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.
CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions
, 2005
"... Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NPcomplete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and ..."
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Cited by 57 (9 self)
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Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NPcomplete 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 bidordering 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 runtime distribution does not have a heavy tail.
Partialrevelation VCG mechanism for combinatorial auctions
 In Proceddings of the National Conference on Artificial Intelligence (AAAI
"... Winner determination in combinatorial auctions has received significant interest in the AI community in the last 3 years. Another difficult problem in combinatorial auctions is that of eliciting the bidders ’ preferences. We introduce a progressive, partialrevelation mechanism that determines an ef ..."
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Cited by 49 (21 self)
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Winner determination in combinatorial auctions has received significant interest in the AI community in the last 3 years. Another difficult problem in combinatorial auctions is that of eliciting the bidders ’ preferences. We introduce a progressive, partialrevelation mechanism that determines an efficient allocation and the Vickrey payments. The mechanism is based on a family of algorithms that explore the natural lattice structure of the bidders ’ combined preferences. The mechanism elicits utilities in a natural sequence, and aims at keeping the amount of elicited information and the effort to compute the information minimal. We present analytical results on the amount of elicitation. We show that no valuequerying algorithm that is constrained to querying feasible bundles can save more elicitation than one of our algorithms. We also show that one of our algorithms can determine the Vickrey payments as a costless byproduct of determining an optimal allocation.
Computational Criticisms of the Revelation Principle
, 2003
"... 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. ..."
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Cited by 44 (12 self)
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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 multistep mechanisms, one can reduce exponential communication and computation to linearthereby answering a recognized important open question in mechanism design. Regarding B, we criticize the focus on truthful mechanismsa 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 availablea 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...
Preference Elicitation and Query Learning
 Journal of Machine Learning Research
, 2004
"... In this paper we explore the relationship between "preference elicitation", a learningstyle 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 th ..."
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Cited by 41 (6 self)
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In this paper we explore the relationship between "preference elicitation", a learningstyle 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 twobidder preference elicitation and query learning, giving both separation results and proving some connections between these problems.
Eliciting Bid Taker Nonprice Preferences in (Combinatorial) Auctions
 IN PROCEEDINGS OF THE NINETEENTH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2004
"... Recent algorithms provide powerful solutions to the problem of determining costminimizing (or revenuemaximizing) 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 relevan ..."
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Cited by 36 (15 self)
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Recent algorithms provide powerful solutions to the problem of determining costminimizing (or revenuemaximizing) 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.