Results 1  10
of
67
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 ..."
Abstract

Cited by 43 (15 self)
 Add to MetaCart
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.
Truthful approximation schemes for singleparameter agents
 In FOCS ’08
"... We present the first monotone randomized polynomialtime approximation scheme (PTAS) for minimizing the makespan of parallel related machines (QCmax), the paradigmatic problem in singleparameter algorithmic mechanism design. This result immediately gives a polynomialtime, truthful (in expectation ..."
Abstract

Cited by 32 (7 self)
 Add to MetaCart
We present the first monotone randomized polynomialtime approximation scheme (PTAS) for minimizing the makespan of parallel related machines (QCmax), the paradigmatic problem in singleparameter algorithmic mechanism design. This result immediately gives a polynomialtime, truthful (in expectation) mechanism whose approximation guarantee attains the bestpossible one for all polynomialtime algorithms (assuming P ̸ = NP). Our algorithmic techniques are flexible and also yield a monotone deterministic quasiPTAS for QCmax and a monotone randomized PTAS for maxmin scheduling on related machines. 1
Incentive compatible regression learning
 IN THE ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2008
"... We initiate the study of incentives in a general machine learning framework. We focus on a gametheoretic regression learning setting where private information is elicited from multiple agents with different, possibly conflicting, views on how to label the points of an input space. This conflict pot ..."
Abstract

Cited by 30 (14 self)
 Add to MetaCart
We initiate the study of incentives in a general machine learning framework. We focus on a gametheoretic regression learning setting where private information is elicited from multiple agents with different, possibly conflicting, views on how to label the points of an input space. This conflict potentially gives rise to untruthfulness on the part of the agents. In the restricted but important case when every agent cares about a single point, and under mild assumptions, we show that agents are motivated to tell the truth. In a more general setting, we study the power and limitations of mechanisms without payments. We finally establish that, in the general setting, the VCG mechanism goes a long way in guaranteeing truthfulness and economic efficiency.
Item Pricing for Revenue Maximization
"... We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected rev ..."
Abstract

Cited by 29 (4 self)
 Add to MetaCart
We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of the total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18], who show a logarithmic factor for only the special cases of singleminded and unitdemand customers. In the limited supply setting, we show that for subadditive valuations, a random single price achieves revenue within a factor of 2 O( √ log n log log n) of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme for subadditive (or even submodular) valuations, even using multiple prices. We complement this result with a lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio 2 Ω(log1/4 n), thus showing that single price schemes cannot achieve a polylogarithmic ratio. This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12, 10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12], and more generally subadditive [10], customers.
A Scheduling Approach to Coalitional Manipulation
"... The coalitional manipulation problem is one of the central problems in computational social choice. In this paper we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008]. Our main result is a p ..."
Abstract

Cited by 28 (12 self)
 Add to MetaCart
The coalitional manipulation problem is one of the central problems in computational social choice. In this paper we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008]. Our main result is a polynomialtime algorithm with (roughly speaking) the following theoretical guarantee: given a manipulable instance with m alternatives the algorithm finds a successful manipulation with at most m − 2 additional manipulators. Our technique is based on a reduction to the scheduling problem known as QpmtnCmax, along with a novel rounding procedure. We demonstrate that our analysis is tight by establishing a new type of integrality gap. We also resolve a known open question in computational social choice by showing that the coalitional manipulation problem remains (strongly) NPcomplete for positional scoring rules even when votes are unweighted. Finally, we discuss the implications of our results with respect to the question: “Is there a prominent voting rule that is usually hard to manipulate?”
On the approximability of Dodgson and Young elections
, 2008
"... The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorith ..."
Abstract

Cited by 24 (11 self)
 Add to MetaCart
The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for approximating the Dodgson score: an LPbased randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an O(log m) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in N P have quasipolynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that
From convex optimization to randomized mechanisms: Toward optimal combinatorial auctions
 In Proceedings of the 43rd annual ACM Symposium on Theory of Computing (STOC
, 2011
"... We design an expected polynomialtime, truthfulinexpectation, (1 − 1/e)approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), which encompass mostconcreteexamplesofsubmodular ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
We design an expected polynomialtime, truthfulinexpectation, (1 − 1/e)approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), which encompass mostconcreteexamplesofsubmodularfunctionsstudiedinthiscontext,includingcoveragefunctions, matroid weightedrank functions, and convex combinations thereof. Our approximation factor is the best possible, even for known and explicitly given coverage valuations, assuming P ̸ = NP. Ours is the first truthfulinexpectation and polynomialtime mechanism to achieve a constantfactor approximation for an NPhard welfare maximization problem in combinatorial auctions with heterogeneous goods and restricted valuations. Our mechanism is an instantiation of a new framework for designing approximation mechanisms based on randomized rounding algorithms. A typical such algorithm first optimizes over a fractional relaxation of the original problem, and then randomly rounds the fractional solution to an integral one. With rare exceptions, such algorithms cannot be converted into truthful mechanisms. The highlevel idea of our mechanism design framework is to optimize directly
BlackBox Randomized Reductions in Algorithmic Mechanism Design
"... Abstract—We give the first blackbox reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a nontrivial class of multiparameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthfulinexpectation randomized mech ..."
Abstract

Cited by 16 (4 self)
 Add to MetaCart
Abstract—We give the first blackbox reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a nontrivial class of multiparameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthfulinexpectation randomized mechanism that is an FPTAS. Our reduction makes novel use of smoothed analysis, by employing small perturbations as a tool in algorithmic mechanism design. We develop a “duality” between linear perturbations of the objective function of an optimization problem and of its feasible set, and use the “primal ” and “dual ” viewpoints to prove the running time bound and the truthfulness guarantee, respectively, for our mechanism.
Socially Desirable Approximations for Dodgson’s Voting Rule ∗ ABSTRACT
"... voting rule that today bears his name. Although Dodgson’s rule is one of the most wellstudied voting rules, it suffers from serious deficiencies, both from the computational point of view—it is N Phard even to approximate the Dodgson score within sublogarithmic factors—and from the social choice p ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
voting rule that today bears his name. Although Dodgson’s rule is one of the most wellstudied voting rules, it suffers from serious deficiencies, both from the computational point of view—it is N Phard even to approximate the Dodgson score within sublogarithmic factors—and from the social choice point of view—it fails basic social choice desiderata such as monotonicity and homogeneity. In a previous paper [Caragiannis et al., SODA 2009] we have asked whether there are approximation algorithms for Dodgson’s rule that are monotonic or homogeneous. In this paper we give definitive answers to these questions. We design a monotonic exponentialtime algorithm that yields a 2approximation to the Dodgson score, while matching this result with a tight lower bound. We also present a monotonic polynomialtime O(log m)approximation algorithm (where
Strategyproof approximation mechanisms for location on networks
 CoRR abs/0907.2049. N
, 2010
"... We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to t ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost. We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a (2 − 2/n)approximation for the social cost, where n is the number of agents, when the network is a circle (known as a ring in the case of computer networks); we design a novel “hybrid” strategyproof randomized mechanism that provides a tight approximation ratio of 3/2 for the maximum