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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 115 (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.
Preference Elicitation in Combinatorial Auctions (Extended Abstract)
 IN PROCEEDINGS OF THE ACM CONFERENCE ON ELECTRONIC COMMERCE (ACMEC
, 2001
"... Combinatorial auctions (CAs) where bidders can bid on bundles of items can be very desirable market mechanisms when the items sold exhibit complementarity and/or substitutability, so the bidder's valuations for bundles are not additive. However, in a basic CA, the bidders may need to bid on expone ..."
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Cited by 100 (28 self)
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Combinatorial auctions (CAs) where bidders can bid on bundles of items can be very desirable market mechanisms when the items sold exhibit complementarity and/or substitutability, so the bidder's valuations for bundles are not additive. However, in a basic CA, the bidders may need to bid on exponentially many bundles, leading to di#culties in determining those valuations, undesirable information revelation, and unnecessary communication. In this paper we present a design of an auctioneer agent that uses topological structure inherent in the problem to reduce the amount of information that it needs from the bidders. An analysis tool is presented as well as data structures for storing and optimally assimilating the information received from the bidders. Using this information, the agent then narrows down the set of desirable (welfaremaximizing or Paretoe#cient) allocations, and decides which questions to ask next. Several algorithms are presented that ask the bidders for value, order, and rank information. A method is presented for making the elicitor incentive compatible.
The Communication Complexity of Efficient Allocation Problems
 DIMACS workshop on Computational Issues in Game Theory and Mechanism Design
, 2001
"... We analyze the communication complexity of surplusmaximizing allocations. We study both the continuous and discrete models of communication, measuring its complexity with the dimensionality of the message space and the number of transmitted bits, respectively. In both cases, we offer a lower bound ..."
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Cited by 34 (2 self)
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We analyze the communication complexity of surplusmaximizing allocations. We study both the continuous and discrete models of communication, measuring its complexity with the dimensionality of the message space and the number of transmitted bits, respectively. In both cases, we offer a lower bound on the amount of communication. This bound is applied to the problem of allocating L heterogeneous objects among N agents, whose valuations are (i) unrestricted, (ii) submodular, or (iii) homogeneous in objects. In cases (i) and (ii), efficiency requires exponential communication in L. Furthermore, in case (i), polynomial communication in L cannot achieve a higher surplus than selling all objects as a bundle. On the other hand, in case (iii), exact efficiency requires the transmission of L numbers, but arbitrarily close approximation is achieved with only O(log L) bits. When a Walrasian equilibrium with peritem prices exists, efficiency is achieved with deterministic communication that is polynomial in L.
The Communication Requirements of Social Choice Rules and Supporting Budget Sets
 Journal of Economic Theory
, 2003
"... The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any communication verifying that an alternative is in the rule must reveal supporting budget sets for the agents such ..."
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Cited by 20 (2 self)
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The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any communication verifying that an alternative is in the rule must reveal supporting budget sets for the agents such that the optimality of the proposed alternative to all agents within their respective budget set in itself verifies the alternative. We characterize the budget equilibria that are the minimally informative messages verifying a given choice rule. This characterization is used to identify the communication burden of choice rules, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisiblegood economies, and stable manytoone matchings.
The communication cost of selfishness
 Journal of Economic Theory
, 2005
"... We consider the amount of communication required to implement a given decision rule when the mechanism must be ex post or Bayesian incentive compatible. In ex post incentive compatibility, the communication protocol must reveal enough information to calculate monetary transfers to the agents to moti ..."
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Cited by 10 (0 self)
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We consider the amount of communication required to implement a given decision rule when the mechanism must be ex post or Bayesian incentive compatible. In ex post incentive compatibility, the communication protocol must reveal enough information to calculate monetary transfers to the agents to motivate them to be honest (agents ’ payoffs areassumedtobequasilinear in such transfers). For Bayesian incentive compatibility, the protocol may need to hide some information from the agents to prevent deviations contingent on the information. In both cases, the selfishness of the agents can substancially increase the communication costs. We provide an exponential upper bound on the communication cost of selfishness, which is tight in the Bayesian setting. Whether this exponential upper bound is ever achieved in the ex post setting remains an open question. We examine some extensions of our initial setting. In particular we show that for the averagecase communication complexity measure, the communication cost of selfishness may be arbitrarily large in both ex post and Bayesian settings. We also examine some special cases in which the communication cost of selfishness proves to be very low, in particular when we want to implement efficiency. 1
The Communication Cost of Selfishness: Ex Post Implementation
"... We consider the communication complexity of implementing a given decision rule when the protocol must also calculate payments to motivate the agents to be honest in an ex post equilibrium (agents payoffs are assumed to be quasilinear in such payments). We find that the communication cost of self ..."
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Cited by 5 (1 self)
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We consider the communication complexity of implementing a given decision rule when the protocol must also calculate payments to motivate the agents to be honest in an ex post equilibrium (agents payoffs are assumed to be quasilinear in such payments). We find that the communication cost of selfishness when measured with the averagecase communication complexity may be arbitrarily large. For the worstcase communication complexity measure, we provide an exponential upper bound on the communication cost of selfishness. Whether this bound is ever achieved remains an open question. We examine several special cases in which the communication cost of selfishness proves to be very low. These include cases where we want to implement efficiency or where we have only two agents, and the precision of agents' utilities is fixed.
On the Communication Requirements of Verifying the VCG Outcome
 EC'08
, 2008
"... We consider the amount of communication required to verify the outcome of the VickreyClarkeGroves (VCG) mechanism: an efficient allocation together with incentivizing VCG payments. We compare this to the communication required to verify the efficient decision rule alone, to assess the overhead imp ..."
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Cited by 3 (1 self)
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We consider the amount of communication required to verify the outcome of the VickreyClarkeGroves (VCG) mechanism: an efficient allocation together with incentivizing VCG payments. We compare this to the communication required to verify the efficient decision rule alone, to assess the overhead imposed by VCG payments. Our characterizations are obtained by leveraging a connection between the VCG outcome and a price equilibrium concept known as universal competitive equilibrium. We consider four related environments within a common framework: the classic singleitem setting, the multiunit setting with decreasing marginal values, the classic assignment problem with unitdemand valuations, and the multiunit assignment problem with substitutes valuations. We find that the singleunit settings have zero overhead, whereas the multiunit settings can have significant positive overhead. With multiple units, the naïve VCG protocol that runs several efficient protocols in sequence (one with all agents, and ones with an agent removed, for each agent) is asymptotically optimal for several parameter settings of the number of agents, commodities, and units.
The Communication Cost of Sel…shness: Ex Post Implementation
, 2005
"... We consider the communication complexity of implementing a given decision rule when the protocol must also calculate payments to motivate the agents to be honest in an ex post equilibrium (agents ’ payo¤s are assumed to be quasilinear in such payments). We …nd that the communication cost of sel…shn ..."
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We consider the communication complexity of implementing a given decision rule when the protocol must also calculate payments to motivate the agents to be honest in an ex post equilibrium (agents ’ payo¤s are assumed to be quasilinear in such payments). We …nd that the communication cost of sel…shness when measured with the averagecase communication complexity may be arbitrarily large. For the worstcase communication complexity measure, we provide an exponential upper bound on the communication cost of sel…shness. Whether this bound is ever achieved remains an open question. We examine several special cases in which the communication cost of sel…shness proves to be very low. These include cases where we want to implement e ¢ ciency or where we have only two agents, and the precision of agents’utilities is …xed. 1
The Communication Burden of Payment Determination
"... In the presence of selfinterested parties, mechanism designers typically aim to achieve their goals (implement a socialchoice function) in an equilibrium. In this paper, we study the cost of such equilibrium requirements in terms of communication, a problem that was recently raised by Fadel and Se ..."
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In the presence of selfinterested parties, mechanism designers typically aim to achieve their goals (implement a socialchoice function) in an equilibrium. In this paper, we study the cost of such equilibrium requirements in terms of communication, a problem that was recently raised by Fadel and Segal (2009). While a certain amount of information x needs to be communicated just for computing the outcome of a certain socialchoice function, an additional amount of communication may be required for computing the equilibriumsupporting payments (when such payments exist). Our main result shows that the total amount of information required for this task can be greater than x by a factor linear in the number of players n, i.e., n · x (under a common normalization assumption). This is the first known lower bound for this problem. In fact, we show that this result holds even in singleparameter domains. On the positive side, we show that certain classic economic domains, namely, singleitem auctions and publicgood mechanisms, only entail a small overhead. Finally, we discuss the case in which the normalization assumption does not hold and leave the readers with several open questions.