41 research outputs found
Sharing the cost of multicast transmissions in wireless networks
AbstractA crucial issue in non-cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network. Each station acts as a selfish agent that may misreport its utility (i.e., the maximum cost it is willing to incur to receive the service, in terms of power consumption) in order to maximize its individual welfare, defined as the difference between its true utility and its charged cost. A provider can discourage such deceptions by using a strategyproof cost sharing mechanism, that is a particular public algorithm that, by forcing the agents to truthfully reveal their utility, starting from the reported utilities, decides who gets the service (the receivers) and at what price. A mechanism is said budget balanced (BB) if the receivers pay exactly the (possibly minimum) cost of the transmission, and β-approximate budget balanced (β-BB) if the total cost charged to the receivers covers the overall cost and is at most β times the optimal one, while it is efficient if it maximizes the sum of the receivers’ utilities minus the total cost over all receivers’ sets. In this paper, we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks, in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or BB when the power assignments are induced by a fixed universal spanning tree, or (3ln(k+1))-BB (k is the number of receivers), otherwise. Then we consider the case in which the stations lay in a d-dimensional Euclidean space and the powers fall as 1/dα, and provide strategyproof mechanisms that are either 1-BB or efficient for α=1 or d=1. Finally, we show the existence of 2(3d-1)-BB strategyproof mechanisms in any d-dimensional space for every α⩾d. For the special case of d=2 such a result can be improved to achieve 12-BB mechanisms
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]
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Hard-to-Manipulate Combinatorial Auctions
Mechanism design provides a framework to solve distributed optimization problems in systems of self-interested agents. The combinatorial auction is one such problem, in which there is a set of discrete items to allocate to agents. Unfortunately, recent results suggest that it is impossible to implement reasonable approximations without losing robustness to manipulation. Furthermore, the Vickrey-Clarke-Groves (VCG) mechanism is known to be vulnerable to manipulation when agents can bid under multiple false names. In this paper we relax incentive constraints and require only that useful manipulation be NP-hard. We prove that any tractable approximation algorithm can be made to produce a hard-to-manipulate (VCG-based) mechanism, providing a useful counterpoint to these negative results. We also show that falsename bid manipulation in the VCG is NP-hard.Engineering and Applied Science
Computational Mechanism Design: A Call to Arms
Game theory has developed powerful tools for analyzing decision making in systems with multiple autonomous actors. These tools, when tailored to computational settings, provide a foundation for building multiagent software systems. This tailoring gives rise to the field of computational mechanism design, which applies economic principles to computer systems design
Cost sharing over combinatorial domains: Complement-free cost functions and beyond
We study mechanism design for combinatorial cost sharing models. Imagine that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost sharing domains until recently [7]. Still, many questions about the interplay between strategyproofness, cost recovery and economic efficiency remain unanswered. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design a scheme of ascending cost sharing mechanisms which is applicable to the combinatorial cost sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, O(1)-budget-balanced and O(Hn)-approximate with respect to the social cost. Further, we show that our mechanism is budget-balanced and Hn-approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general only guarantees a poor social cost approximation of n. We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost sharing problems, including Vertex Cover and Set Cover
Cost sharing over combinatorial domains
We study the problem of designing cost-sharing mechanisms for combinatorial domains. Suppose that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost-sharing domains until recently [9]. Still, many questions about the interplay between strategyproofness, cost recovery, and economic efficiency remain unanswered.The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions, which capture the behavior of their average cost-shares.Based on our trace-monotonicity property, we design an Iterative Ascending Cost-Sharing Mechanism, which is applicable to the combinatorial cost-sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, O(1)-budget-balanced, and O(Hn)-approximate with respect to the social cost. Furthermore, we show that our mechanism is budget-balanced and Hn-approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible.Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general, only guarantees a poor social cost approximation of n. We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost-sharing problems, including Vertex Cover and Set Cover
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