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42
Mechanism design via differential privacy
 Proceedings of the 48th Annual Symposium on Foundations of Computer Science
, 2007
"... We study the role that privacypreserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differen ..."
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Cited by 103 (3 self)
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We study the role that privacypreserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differential privacy [15, 14], in addition to its own intrinsic virtue, can ensure that participants have limited effect on the outcome of the mechanism, and as a consequence have limited incentive to lie. More precisely, mechanisms with differential privacy are approximate dominant strategy under arbitrary player utility functions, are automatically resilient to coalitions, and easily allow repeatability. We study several special cases of the unlimited supply auction problem, providing new results for digital goods auctions, attribute auctions, and auctions with arbitrary structural constraints on the prices. As an important prelude to developing a privacypreserving auction mechanism, we introduce and study a generalization of previous privacy work that accommodates the high sensitivity of the auction setting, where a single participant may dramatically alter the optimal fixed price, and a slight change in the offered price may take the revenue from optimal to zero. 1
Rationality and Traffic Attraction: Incentives for Honest Path Announcements in BGP
, 2008
"... We study situations in which autonomous systems (ASes) may have incentives to send BGP announcements differing from the ASlevel paths that packets traverse in the data plane. Prior work on this issue assumed that ASes seek only to obtain the best possible outgoing path for their traffic. In reality ..."
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Cited by 28 (6 self)
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We study situations in which autonomous systems (ASes) may have incentives to send BGP announcements differing from the ASlevel paths that packets traverse in the data plane. Prior work on this issue assumed that ASes seek only to obtain the best possible outgoing path for their traffic. In reality, other factors can influence a rational AS’s behavior. Here we consider a more natural model, in which an AS is also interested in attracting incoming traffic (e.g., because other ASes pay it to carry their traffic). We ask what combinations of BGP enhancements and restrictions on routing policies can ensure that ASes have no incentive to lie about their dataplane paths. We find that protocols like SBGP alone are insufficient, but that SBGP does suffice if coupled with additional (quite unrealistic) restrictions on routing policies. Our gametheoretic analysis illustrates the high cost of ensuring that the ASes honestly announce dataplane paths in their BGP path announcements.
Matroids, Secretary Problems, and Online Mechanisms
"... We study a generalization of the classical secretary problem which we call the “matroid secretary problem”. In this problem, the elements of a matroid are presented to an online algorithm in random order. When an element arrives, the algorithm observes its value and must make an irrevocable decision ..."
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Cited by 24 (4 self)
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We study a generalization of the classical secretary problem which we call the “matroid secretary problem”. In this problem, the elements of a matroid are presented to an online algorithm in random order. When an element arrives, the algorithm observes its value and must make an irrevocable decision regarding whether or not to accept it. The accepted elements must form an independent set, and the objective is to maximize the combined value of these elements. This paper presents an O(log k)competitive algorithm for general matroids (where k is the rank of the matroid), and constantcompetitive algorithms for several special cases including graphic matroids, truncated partition matroids, and bounded degree transversal matroids. We leave as an open question the existence of constantcompetitive algorithms for general matroids. Our results have applications in welfaremaximizing online mechanism design for domains in which the sets of simultaneously satisfiable agents form a matroid.
Singlevalue combinatorial auctions and algorithmic implementation in undominated strategies
 In ACM Symposium on Discrete Algorithms
, 2011
"... In this paper we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple ..."
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Cited by 18 (2 self)
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In this paper we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple the algorithmic allocation problem from the strategic aspects, by a procedure that converts any algorithm to a dominantstrategy ascending mechanism. This technique works for any single value domain, in which each agent has the same value for each desired outcome, and this value is the only private information. In particular, for “singlevalue CAs”, where each player desires any one of several different bundles but has the same value for each of them, our technique converts any approximation algorithm to a dominant strategy mechanism that almost preserves the original approximation ratio. Our second result provides the first computationally efficient deterministic mechanism for the case of singlevalue multiminded bidders (with private value and private desired bundles). The mechanism achieves an approximation to the social welfare which is close to the best possible in polynomial time (unless P=NP). This mechanism is an algorithmic implementation in undominated strategies, a notion that we define and justify, and is of independent interest. 1
Automated online mechanism design and prophet inequalities
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2007
"... Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the ..."
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Cited by 17 (5 self)
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Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many realworld applications (such as online ticket sales), the opposite is true: the seller has distributional knowledge of the bid values (e.g., via the history of past transactions in the market), but there is uncertainty about market size. Adopting the perspective of automated mechanism design, introduced by Conitzer and Sandholm, we develop algorithms that compute an optimal, or approximately optimal, online auction mechanism given access to this distributional knowledge. Our main results are twofold. First, we show that when the seller does not know the market size, no constantapproximation to the optimum efficiency or revenue is achievable in the worst case, even under the very strong assumption that bid values are i.i.d. samples from a distribution known to the seller. Second, we show that when the seller has distributional knowledge of the market size as well as the bid values, one can do well in several senses. Perhaps most interestingly, by combining dynamic programming with prophet inequalities (a technique from optimal stopping theory) we are able to design and analyze online mechanisms which are temporally strategyproof (even with respect to arrival and departure times) and approximately efficiency(revenue)maximizing. In exploring the interplay between automated mechanism design and prophet inequalities, we prove new prophet inequalities motivated by the auction setting.
Fairness with an honest minority and a rational majority. Cryptology ePrint Archive, Report 2008/097
, 2008
"... Abstract. We provide a simple protocol for secret reconstruction in any threshold secret sharing scheme, and prove that it is fair when executed with many rational parties together with a small minority of honest parties. That is, all parties will learn the secret with high probability when the hone ..."
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Cited by 16 (3 self)
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Abstract. We provide a simple protocol for secret reconstruction in any threshold secret sharing scheme, and prove that it is fair when executed with many rational parties together with a small minority of honest parties. That is, all parties will learn the secret with high probability when the honest parties follow the protocol and the rational parties act in their own selfinterest (as captured by a setNash analogue of trembling hand perfect equilibrium). The protocol only requires a standard (synchronous) broadcast channel, tolerates both early stopping and incorrectly computed messages, and only requires 2 rounds of communication. Previous protocols for this problem in the cryptographic or economic models have either required an honest majority, used strong communication channels that enable simultaneous exchange of information, or settled for approximate notions of security/equilibria. They all also required a nonconstant number of rounds of communication.
Algorithms for rationalizability and CURB sets
 IN: PROCEEDINGS OF THE TWENTYFIRST NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2006
"... Significant work has been done on computational aspects of solving games under various solution concepts, such as Nash equilibrium, subgame perfect Nash equilibrium, correlated equilibrium, and (iterated) dominance. However, the fundamental ..."
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Cited by 13 (3 self)
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Significant work has been done on computational aspects of solving games under various solution concepts, such as Nash equilibrium, subgame perfect Nash equilibrium, correlated equilibrium, and (iterated) dominance. However, the fundamental
Characterizing truthful multiarmed bandit mechanisms
 In ACMEC
, 2009
"... We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. I ..."
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Cited by 13 (0 self)
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We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer’s goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the multiarmed bandit problem, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by regret, the difference in social welfare between the algorithm and the benchmark which always selects the same“best”advertisement. We investigate how the design of multiarmed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties – essentially, they must separate exploration from exploitation – and they incur much higher regret than the optimal multiarmed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.
Secretary Problems: Weights and Discounts
"... The classical secretary problem studies the problem of selecting online an element (a “secretary”) with maximum value in a randomly ordered sequence. The difficulty lies in the fact that an element must be either selected or discarded upon its arrival, and this decision is irrevocable. Constantcomp ..."
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Cited by 12 (3 self)
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The classical secretary problem studies the problem of selecting online an element (a “secretary”) with maximum value in a randomly ordered sequence. The difficulty lies in the fact that an element must be either selected or discarded upon its arrival, and this decision is irrevocable. Constantcompetitive algorithms are known for the classical secretary problems (see, e.g., the survey of Freeman [7]) and several variants. We study the following two extensions of the secretary problem: • In the discounted secretary problem, there is a timedependent “discount ” factor d(t), and the benefit derived from selecting an element/secretary e at time t is d(t)·v(e). For this problem with arbitrary (not necessarily decreasing) functions d(t), we show a constantcompetitive algorithm when the expected optimum is known in advance. With no prior knowledge, log n we exhibit a lower bound of Ω (), and give a nearlylog log n matching O(log n)competitive algorithm. • In the weighted secretary problem, up to K secretaries can be selected; when a secretary is selected (s)he must be irrevocably assigned to one of K positions, with position k having weight w(k), and assigning object/secretary e to position k has benefit w(k) · v(e). The goal is to select secretaries and assign them to positions to maximize ∑ e,k w(k) · v(e) · xek where xek is an indicator variable that secretary e is assigned position k. We give constantcompetitive algorithms for this problem. Most of these results can also be extended to the matroid secretary case (Babaioff et al. [2]) for a large family of matroids with a constantfactor loss, and an O(log rank) loss for general matroids. These results are based on a reduction from various matroids to partition matroids which present a unified approach to many of the upper bounds of Babaioff et al. These problems have connections to online mechanism design (see, e.g., Hajiaghayi et al. [9]). All our algorithms are monotone, and hence lead to truthful mechanisms for the corresponding online auction problems. 1
Dynamic Pricing for Impatient Bidders
"... We study the following problem related to pricing over time. Assume there is a collection of bidders, each of whom is interested in buying a copy of an item of which there is an unlimited supply. Every bidder is associated with a time interval over which the bidder will consider buying a copy of the ..."
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Cited by 10 (1 self)
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We study the following problem related to pricing over time. Assume there is a collection of bidders, each of whom is interested in buying a copy of an item of which there is an unlimited supply. Every bidder is associated with a time interval over which the bidder will consider buying a copy of the item, and a maximum value the bidder is willing to pay for the item. On every time unit the seller sets a price for the item. The seller’s goal is to set the prices so as to maximize revenue from the sale of copies of items over the time period. In the first model considered we assume that all bidders are impatient, that is, bidders buy the item at the first time unit within their bid interval that they can afford the price. To the best of our knowledge, this is the first work that considers this model. In the offline setting we assume that the seller knows the bids of all the bidders in advance. In the online setting we assume that at each time unit the seller only knows the values of the bids that have arrived before or at that time unit. We give a polynomial time offline algorithm and prove upper and lower bounds on the competitiveness of deterministic and randomized online algorithms, compared with the optimal offline solution. The gap between the upper and lower bounds is quadratic. We also consider the envy free model in which bidders are sold the item at the minimum price during their bid interval, as long as it is not over their limit value. We prove tight bounds on the competitiveness of deterministic online algorithms for this model, and upper and lower bounds on the competitiveness of randomized algorithms with quadratic gap. The lower bounds for the randomized case in both models uses a novel general technique.