Results 1  10
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36
Computationally feasible VCG mechanisms
 In Proceedings of the Second ACM Conference on Electronic Commerce (EC’00
, 2000
"... A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore comp ..."
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Cited by 188 (5 self)
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A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore computationally infeasible. However, if the optimal outcome is replaced by the results of a suboptimal algorithm, the resulting mechanism (termed VCGbased) is no longer necessarily truthful. The first part of this paper studies this phenomenon in depth and shows that it is near 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 nontruthful VCGbased mechanisms. We generalize these results for affine maximizers. The second part of this paper proposes a general method for circumventing the above problem. We introduce a modification of VCGbased mechanisms in which the agents are given a chance to improve the output of the underlying algorithm. When the agents behave truthfully, the welfare obtained by the mechanism is at least as good as the one obtained by the algorithm’s output. We provide a strong rationale for truthtelling behavior. Our method satisfies individual rationality as well.
The communication requirements of efficient allocations and supporting prices
 Journal of Economic Theory
, 2006
"... We show that any communication finding a Pareto efficient allocation in a privateinformation economy must also discover supporting Lindahl prices. In particular, efficient allocation of L indivisible objects requires naming a price for each of the 2 L ¡1 bundles. Furthermore, exponential communicat ..."
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Cited by 113 (15 self)
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We show that any communication finding a Pareto efficient allocation in a privateinformation economy must also discover supporting Lindahl prices. In particular, efficient allocation of L indivisible objects requires naming a price for each of the 2 L ¡1 bundles. Furthermore, exponential communication in L is needed just to ensure a higher share of surplus than that realized by auctioning all items as a bundle, or even a higher expected surplus (for some probability distribution over valuations). When the valuations are submodular, efficiency still requires exponential communication (and fully polynomial approximation is impossible). When the objects are homogeneous, arbitrarily good approximation is obtained using exponentially less communication than that needed for exact efficiency.
Truthful approximation mechanisms for restricted combinatorial auctions
, 2002
"... When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCGlike payment rules will not ensure truthfulness). We dev ..."
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Cited by 94 (3 self)
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When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCGlike payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann O’Callaghan, and Shoham, who presented greedy heuristics. We show how to use IFTHENELSE constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios. 1
Incentive compatible multi unit combinatorial auctions
 In TARK 03
, 2003
"... This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each g ..."
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Cited by 90 (10 self)
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This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both online and offline scenarios. This is the first result where nonVCG mechanisms are derived for nonsingle minded bidders for a natural model of combinatorial auctions.
Efficient learning equilibrium
 In Proceedings of NIPS
, 2002
"... We introduce ecient learning equilibrium (ELE), a normative approach to learning in noncooperative settings. In ELE, the learning algorithms themselves are required to be in equilibrium. In addition, the learning algorithms must arrive at a desired value after polynomial time, and a deviation from ..."
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Cited by 45 (6 self)
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We introduce ecient learning equilibrium (ELE), a normative approach to learning in noncooperative settings. In ELE, the learning algorithms themselves are required to be in equilibrium. In addition, the learning algorithms must arrive at a desired value after polynomial time, and a deviation from the prescribed ELE become irrational after polynomial time. We prove the existence of an ELE (where the desired value is the expected payoff in a Nash equilibrium) and of a ParetoELE (where the objective is the maximization of social surplus) in repeated games with perfect monitoring. We also show that an ELE does not always exist in the imperfect monitoring case. Finally, we discuss the extension of these results to generalsum stochastic games.
Approximate Mechanism Design Without Money
, 2009
"... The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforc ..."
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Cited by 43 (15 self)
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The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity. We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.
Inapproximability results for combinatorial auctions with submodular utility functions
 in Proceedings of WINE 2005
, 2005
"... We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodu ..."
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Cited by 36 (0 self)
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We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1 − 1/e � 0.632, unless P = NP. Our result is based on a reduction from a multiprover proof system for MAX3COLORING. 1
Robust game theory
, 2006
"... We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides ..."
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Cited by 33 (0 self)
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We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides an alternative distributionfree equilibrium concept, which we call “robustoptimization equilibrium, ” to that of the ex post equilibrium. We prove that the robustoptimization equilibria of an incompleteinformation game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robustoptimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results.
Regret Minimizing Equilibria and Mechanisms for Games with Strict Type Uncertainty
 In Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence
, 2004
"... Mechanism design has found considerable application to the construction of agentinteraction protocols. In the standard setting, the type (e.g., utility function) of an agent is not known by other agents, nor is it known by the mechanism designer. When this uncertainty is quantified probabilisticall ..."
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Cited by 32 (4 self)
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Mechanism design has found considerable application to the construction of agentinteraction protocols. In the standard setting, the type (e.g., utility function) of an agent is not known by other agents, nor is it known by the mechanism designer. When this uncertainty is quantified probabilistically, a mechanism induces a game of incomplete information among the agents. However, in many settings, uncertainty over utility functions cannot easily be quantified. We consider the problem of incomplete information games in which type uncertainty is strict or unquantified. We propose the use of minimax regret as a decision criterion in such games, a robust approach for dealing with type uncertainty. We define minimaxregret equilibria and prove that these exist in mixed strategies for finite games. We also consider the problem of mechanism design in this framework by adopting minimax regret as an optimization criterion for the designer itself, and study automated optimization of such mechanisms. 1
Tight informationtheoretic lower bounds for welfare maximization in combinatorial auctions
 Proc. of ACM EC
, 2007
"... We provide tight informationtheoretic lower bounds for the welfare maximization problem in combinatorial auctions. In this problem the goal is to partition m items between k bidders in a way that maximizes the sum of bidders ’ values for their allocated items. Bidders have complex preferences over ..."
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Cited by 31 (7 self)
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We provide tight informationtheoretic lower bounds for the welfare maximization problem in combinatorial auctions. In this problem the goal is to partition m items between k bidders in a way that maximizes the sum of bidders ’ values for their allocated items. Bidders have complex preferences over items expressed by valuation functions that assign values to all subsets of items. We study the “black box ” setting in which the auctioneer has oracle access to the valuation functions of the bidders. In particular, we explore the wellknown value queries model in which the permitted query to a valuation function is in the form of a subset of items, and the reply is the value assigned to that subset of items by the valuation function. We consider different classes of valuation functions: Submodular, subadditive, and superadditive. For these classes it has been shown that one can achieve approximation ratios of 1 − 1 e, √1, and m √ log m m, respectively, via a polynomial (in n and m) number of value queries. We prove that these approximation factors are essentially the best possible: For any fixed ɛ> 0, a (1 − 1/e + ɛ)approximation for submodular valuations or an 1 m 1/2−ɛapproximation for subadditive valuations would require exponentially many value queries, and a log1+ɛ m mapproximation for superadditive valuations would require a superpolynomial number of value queries.