64 research outputs found
Set-Monotonicity Implies Kelly-Strategyproofness
This paper studies the strategic manipulation of set-valued social choice
functions according to Kelly's preference extension, which prescribes that one
set of alternatives is preferred to another if and only if all elements of the
former are preferred to all elements of the latter. It is shown that
set-monotonicity---a new variant of Maskin-monotonicity---implies
Kelly-strategyproofness in comprehensive subdomains of the linear domain.
Interestingly, there are a handful of appealing Condorcet extensions---such as
the top cycle, the minimal covering set, and the bipartisan set---that satisfy
set-monotonicity even in the unrestricted linear domain, thereby answering
questions raised independently by Barber\`a (1977) and Kelly (1977).Comment: 14 page
Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations
Cake cutting is one of the most fundamental settings in fair division and
mechanism design without money. In this paper, we consider different levels of
three fundamental goals in cake cutting: fairness, Pareto optimality, and
strategyproofness. In particular, we present robust versions of envy-freeness
and proportionality that are not only stronger than their standard
counter-parts but also have less information requirements. We then focus on
cake cutting with piecewise constant valuations and present three desirable
algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium
Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time,
robust envy-free, and non-wasteful. It relies on parametric network flows and
recent generalizations of the probabilistic serial algorithm. For the subdomain
of piecewise uniform valuations, we show that it is also group-strategyproof.
Then, we show that there exists an algorithm (MEA) that is polynomial-time,
envy-free, proportional, and Pareto optimal. MEA is based on computing a
market-based equilibrium via a convex program and relies on the results of
Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA
and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise
uniform valuations. We then present an algorithm CSD and a way to implement it
via randomization that satisfies strategyproofness in expectation, robust
proportionality, and unanimity for piecewise constant valuations. For the case
of two agents, it is robust envy-free, robust proportional, strategyproof, and
polynomial-time. Many of our results extend to more general settings in cake
cutting that allow for variable claims and initial endowments. We also show a
few impossibility results to complement our algorithms.Comment: 39 page
Finding Preference Profiles of Condorcet Dimension via SAT
Condorcet winning sets are a set-valued generalization of the well-known
concept of a Condorcet winner. As supersets of Condorcet winning sets are
always Condorcet winning sets themselves, an interesting property of preference
profiles is the size of the smallest Condorcet winning set they admit. This
smallest size is called the Condorcet dimension of a preference profile. Since
little is known about profiles that have a certain Condorcet dimension, we show
in this paper how the problem of finding a preference profile that has a given
Condorcet dimension can be encoded as a satisfiability problem and solved by a
SAT solver. Initial results include a minimal example of a preference profile
of Condorcet dimension 3, improving previously known examples both in terms of
the number of agents as well as alternatives. Due to the high complexity of
such problems it remains open whether a preference profile of Condorcet
dimension 4 exists.Comment: Corrected typos, updated references, and added conclusio
Generalized Incremental Mechanisms for Scheduling Games
We study the problem of devising truthful mechanisms for cooperative cost sharing
games that realize (approximate) budget balance and social cost. Recent negative
results show that group-strategyproof mechanisms can only achieve very poor approximation
guarantees for several fundamental cost sharing games. Driven by these limitations,
we consider cost sharing mechanisms that realize the weaker notion of weak groupstrategyproofness.
Mehta et al. [Games and Economic Behavior, 67:125–155, 2009] recently
introduced the broad class of weakly group-strategyproof acyclic mechanisms and
show that several primal-dual approximation algorithms naturally give rise to such mechanisms
with attractive approximation guarantees. In this paper, we provide a simple yet
powerful approach that enables us to turn any r-approximation algorithm into a r-budget
balanced acyclic mechanism. We demonstrate the applicability of our approach by deriving
weakly group-strategyproof mechanisms for several fundamental scheduling problems
that outperform the best possible approximation guarantees of Moulin mechanisms.
The mechanisms that we develop for completion time scheduling problems are the first
mechanisms that achieve constant budget balance and social cost approximation factors.
Interestingly, our mechanisms belong to the class of generalized incremental mechanisms
proposed by Moulin [Social Choice and Welfare, 16:279–320, 1999]
Computing with strategic agents
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 179-189).This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privately-known value for any particular allocation. A mechanism is truthful if it is in each participant's best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multi-unit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings - the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices.(cont.) Randomization in truthful mechanism design is undesirable because, in arguing the truthfulness of the mechanism, we employ an underlying assumption that the bidders trust the random coin flips of the auctioneer. Despite conjectures to the contrary, we are able to design a technique to derandomize any multi-unit auction in the limited demand case without losing much of the revenue guarantees. We then consider the limited budget case and provide the first competitive auction for this setting, although our auction is randomized. Next, we consider abandoning truthfulness in order to improve the revenue properties of procurement auctions, or auctions that are used to hire a team of agents to complete a task. We study first-price procurement auctions and their variants and argue that in certain settings the payment is never significantly more than, and sometimes much less than, truthful mechanisms. Then we consider the setting of cost-sharing auctions. In a cost-sharing auction, agents bid to receive some service, such as connectivity to the Internet. A subset of agents is then selected for service and charged prices to approximately recover the cost of servicing them.(cont.) We ask what can be achieved by cost -sharing auctions satisfying a strengthening of truthfulness called group-strategyproofness. Group-strategyproofness requires that even coalitions of agents do not have an incentive to report bids other than their true values in the absence of side-payments. For a particular class of such mechanisms, we develop a novel technique based on the probabilistic method for proving bounds on their revenue and use this technique to derive tight or nearly-tight bounds for several combinatorial optimization games. Our results are quite pessimistic, suggesting that for many problems group-strategyproofness is incompatible with revenue goals. Finally, we study centralized two-sided markets, or markets that form a matching between participants based on preference lists. We consider mechanisms that output matching which are stable with respect to the submitted preferences. A matching is stable if no two participants can jointly benefit by breaking away from the assigned matching to form a pair.(cont.) For such mechanisms, we are able to prove that in a certain probabilistic setting each participant's best strategy is truthfulness with high probability (assuming other participants are truthful as well) even though in such markets in general there are provably no truthful mechanisms.by Nicole Immorlica.Ph.D
Practical algorithms and experimentally validated incentives for equilibrium-based fair division (A-CEEI)
Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is an
equilibrium-based solution concept for fair division of discrete items to
agents with combinatorial demands. In theory, it is known that in
asymptotically large markets:
1. For incentives, the A-CEEI mechanism is Envy-Free-but-for-Tie-Breaking
(EF-TB), which implies that it is Strategyproof-in-the-Large (SP-L).
2. From a computational perspective, computing the equilibrium solution is
unfortunately a computationally intractable problem (in the worst-case,
assuming ).
We develop a new heuristic algorithm that outperforms the previous
state-of-the-art by multiple orders of magnitude. This new, faster algorithm
lets us perform experiments on real-world inputs for the first time. We
discover that with real-world preferences, even in a realistic implementation
that satisfies the EF-TB and SP-L properties, agents may have surprisingly
simple and plausible deviations from truthful reporting of preferences. To this
end, we propose a novel strengthening of EF-TB, which dramatically reduces the
potential for strategic deviations from truthful reporting in our experiments.
A (variant of) our algorithm is now in production: on real course allocation
problems it is much faster, has zero clearing error, and has stronger incentive
properties than the prior state-of-the-art implementation.Comment: To appear in EC 202
Approximation algorithms for distributed and selfish agents
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 157-165).Many real-world systems involve distributed and selfish agents who optimize their own objective function. In these systems, we need to design efficient mechanisms so that system-wide objective is optimized despite agents acting in their own self interest. In this thesis, we develop approximation algorithms and decentralized mechanisms for various combinatorial optimization problems in such systems. First, we investigate the distributed caching and a general set of assignment problems. We develop an almost tight LP-based ... approximation algorithm and a local search ... approximation algorithm for these problems. We also design efficient decentralized mechanisms for these problems and study the convergence of the corresponding games. In the following chapters, we study the speed of convergence to high quality solutions on (random) best-response paths of players. First, we study the average social value on best response paths in basic-utility, market sharing, and cut games. Then, we introduce the sink equilibrium as a new equilibrium concept. We argue that, unlike Nash equilibria, the selfish behavior of players converges to sink equilibria and all strategic games have a sink equilibrium. To illustrate the use of this new concept, we study the social value of sink equilibria in weighted selfish routing (or weighted congestion) games and valid-utility (or submodular-utility) games. In these games, we bound the average social value on random best-response paths for sink equilibria.. Finally, we study cross-monotonic cost sharings and group-strategyproof mechanisms.(cont.) We study the limitations imposed by the cross-monotonicity property on cost-sharing schemes for several combinatorial optimization games including set cover and metric facility location. We develop a novel technique based on the probabilistic method for proving upper bounds on the budget-balance factor of cross-monotonic cost sharing schemes, deriving tight or nearly-tight bounds for these games. At the end, we extend some of these results to group-strategyproof mechanisms.by Vahab S. Mirrokni.Ph.D
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