105,252 research outputs found
Mechanism Design without Money via Stable Matching
Mechanism design without money has a rich history in social choice
literature. Due to the strong impossibility theorem by Gibbard and
Satterthwaite, exploring domains in which there exist dominant strategy
mechanisms is one of the central questions in the field. We propose a general
framework, called the generalized packing problem (\gpp), to study the
mechanism design questions without payment. The \gpp\ possesses a rich
structure and comprises a number of well-studied models as special cases,
including, e.g., matroid, matching, knapsack, independent set, and the
generalized assignment problem.
We adopt the agenda of approximate mechanism design where the objective is to
design a truthful (or strategyproof) mechanism without money that can be
implemented in polynomial time and yields a good approximation to the socially
optimal solution. We study several special cases of \gpp, and give constant
approximation mechanisms for matroid, matching, knapsack, and the generalized
assignment problem. Our result for generalized assignment problem solves an
open problem proposed in \cite{DG10}.
Our main technical contribution is in exploitation of the approaches from
stable matching, which is a fundamental solution concept in the context of
matching marketplaces, in application to mechanism design. Stable matching,
while conceptually simple, provides a set of powerful tools to manage and
analyze self-interested behaviors of participating agents. Our mechanism uses a
stable matching algorithm as a critical component and adopts other approaches
like random sampling and online mechanisms. Our work also enriches the stable
matching theory with a new knapsack constrained matching model
Truthful Assignment without Money
We study the design of truthful mechanisms that do not use payments for the
generalized assignment problem (GAP) and its variants. An instance of the GAP
consists of a bipartite graph with jobs on one side and machines on the other.
Machines have capacities and edges have values and sizes; the goal is to
construct a welfare maximizing feasible assignment. In our model of private
valuations, motivated by impossibility results, the value and sizes on all
job-machine pairs are public information; however, whether an edge exists or
not in the bipartite graph is a job's private information.
We study several variants of the GAP starting with matching. For the
unweighted version, we give an optimal strategyproof mechanism; for maximum
weight bipartite matching, however, we show give a 2-approximate strategyproof
mechanism and show by a matching lowerbound that this is optimal. Next we study
knapsack-like problems, which are APX-hard. For these problems, we develop a
general LP-based technique that extends the ideas of Lavi and Swamy to reduce
designing a truthful mechanism without money to designing such a mechanism for
the fractional version of the problem, at a loss of a factor equal to the
integrality gap in the approximation ratio. We use this technique to obtain
strategyproof mechanisms with constant approximation ratios for these problems.
We then design an O(log n)-approximate strategyproof mechanism for the GAP by
reducing, with logarithmic loss in the approximation, to our solution for the
value-invariant GAP. Our technique may be of independent interest for designing
truthful mechanisms without money for other LP-based problems.Comment: Extended abstract appears in the 11th ACM Conference on Electronic
Commerce (EC), 201
Verifiably Truthful Mechanisms
It is typically expected that if a mechanism is truthful, then the agents
would, indeed, truthfully report their private information. But why would an
agent believe that the mechanism is truthful? We wish to design truthful
mechanisms, whose truthfulness can be verified efficiently (in the
computational sense). Our approach involves three steps: (i) specifying the
structure of mechanisms, (ii) constructing a verification algorithm, and (iii)
measuring the quality of verifiably truthful mechanisms. We demonstrate this
approach using a case study: approximate mechanism design without money for
facility location
Heterogeneous Facility Location without Money
The study of the facility location problem in the presence of self-interested agents has recently emerged as the benchmark problem in the research on mechanism design without money. In the setting studied in the literature so far, agents are single-parameter in that their type is a single number encoding their position on a real line. We here initiate a more realistic model for several real-life scenarios. Specifically, we propose and analyze heterogeneous facility location without money, a novel model wherein: (i) we have multiple heterogeneous (i.e., serving different purposes) facilities, (ii) agents' locations are disclosed to the mechanism and (iii) agents bid for the set of facilities they are interested in (as opposed to bidding for their position on the network).
We study the heterogeneous facility location problem under two different objective functions, namely: social cost (i.e., sum of all agents' costs) and maximum cost. For either objective function, we study the approximation ratio of both deterministic and randomized truthful algorithms under the simplifying assumption that the underlying network topology is a line. For the social cost objective function, we devise an (n-1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm. As regards the maximum cost objective function, we propose a 3-approximate deterministic strategyproof algorithm, and prove a 3/2 approximation lower bound for deterministic strategyproof mechanisms. Furthermore, we propose a 3/2-approximate randomized strategyproof algorithm and prove a 4/3 approximation lower bound for randomized strategyproof algorithms
Truthful approximations to range voting
We consider the fundamental mechanism design problem of approximate social
welfare maximization under general cardinal preferences on a finite number of
alternatives and without money. The well-known range voting scheme can be
thought of as a non-truthful mechanism for exact social welfare maximization in
this setting. With m being the number of alternatives, we exhibit a randomized
truthful-in-expectation ordinal mechanism implementing an outcome whose
expected social welfare is at least an Omega(m^{-3/4}) fraction of the social
welfare of the socially optimal alternative. On the other hand, we show that
for sufficiently many agents and any truthful-in-expectation ordinal mechanism,
there is a valuation profile where the mechanism achieves at most an
O(m^{-{2/3}) fraction of the optimal social welfare in expectation. We get
tighter bounds for the natural special case of m = 3, and in that case
furthermore obtain separation results concerning the approximation ratios
achievable by natural restricted classes of truthful-in-expectation mechanisms.
In particular, we show that for m = 3 and a sufficiently large number of
agents, the best mechanism that is ordinal as well as mixed-unilateral has an
approximation ratio between 0.610 and 0.611, the best ordinal mechanism has an
approximation ratio between 0.616 and 0.641, while the best mixed-unilateral
mechanism has an approximation ratio bigger than 0.660. In particular, the best
mixed-unilateral non-ordinal (i.e., cardinal) mechanism strictly outperforms
all ordinal ones, even the non-mixed-unilateral ordinal ones
What to Verify for Optimal Truthful Mechanisms without Money
We aim at identifying a minimal set of conditions under which algorithms with good approximation guarantees are truthful without money. In line with recent literature, we wish to express such a set via verification assumptions, i.e., kind of agents' misbehavior that can be made impossible by the designer.
We initiate this research endeavour for the paradigmatic problem in approximate mechanism design without money, facility location. It is known how truthfulness imposes (even severe) losses and how certain notions of verification are unhelpful in this setting; one is thus left powerless to solve this problem satisfactorily in presence of selfish agents. We here address this issue and characterize the minimal set of verification assumptions needed for the truthfulness of optimal algorithms, for both social cost and max cost objective functions. En route, we give a host of novel conceptual and technical contributions ranging from topological notions of verification to a lower bounding technique for truthful mechanisms that connects methods to test truthfulness (i.e., cycle monotonicity) with approximation guarantee
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