Black-box reductions for cost-sharing mechanism design

Black-box reductions for cost-sharing mechanism design

A cost-sharing mechanism is a protocol that collects bids from a set of players, selects a subset of the players to receive a service (incurring a subset-dependent cost), and determines a price to charge each of these players. Three standard requirements for cost-sharing mechanisms are incentive compatibility, which states that players are motivated to bid their true valuation for the service; budget-balance, meaning that the prices charged should recover the cost incurred; and efficiency, which states that the cost incurred and the valuations of the players served should be traded off in an optimal way. These three goals have been known to be mutually incompatible for thirty years. As a result, nearly all work on cost-sharing mechanisms in the economics and theoretical computer science literatures has focused on achieving two of these goals while completely ignoring the third.We show that incentive-compatibility, budget-balance, and approximate efficiency are simultaneously achievable for a wide range of cost functions, where efficiency is measured using the social cost---the sum of the incurred service cost and the excluded valuations. In particular, we prove such guarantees for well-known mechanisms for all submodular cost functions and for the Steiner tree cost function. We also prove a generic, quantifiable trade-off between the objectives of efficiency and budget-balance in groupstrategyproof cost-sharing mechanisms.

In this paper, we focus on the facility location games with the property of dual preference. Dual preference property indicates that both two preferences of agents, staying close to and staying away from the facility(s), exist in the facility location game. We will explore two types of facility location games with this property, the dual character facility location game and the two-opposite-facility location game with limited distance which model the scenarios in real life. For both of them, we wish to design strategy proof mechanisms or group strategy-proof mechanisms with the objective of optimizing the social utility. For the dual character facility location game, we propose a strategy proof optimal mechanism when misreporting is restricted to agents' preferences, and give a 1/3-approximation deterministic group strategy-proof mechanism when both location and preference are considered as private information. For the two-opposite-facility location game with limited distance, when the number of agents is even (denoted as 2k), we give a 1/k-approximation deterministic group strategy-proof mechanism, and when the number of agents is odd (denoted as 2k-1), we propose a 1/(2k-1)-approximation deterministic group strategy-proof mechanism. The approximation ratios for both mechanisms are proved to be the best a deterministic strategy-proof mechanism can achieve.

In this paper, we consider randomized truthful mechanisms forscheduling tasks to unrelated machines, where each machine iscontrolled by a selfish agent. Some previous work on this topicfocused on a special case, scheduling two machines, for which thebest approximation ratio is 1.6737 [5] and the best lower bound is1.5 [6]. For this case, we give a unified framework for designinguniversally truthful mechanisms, which includes all the knownmechanisms, and also a tight analysis method of their approximationratios. Based on this, we give an improved randomized truthfulmechanism, whose approximation ratio is 1.5963. For the generalcase, when there are m machines, the only known technique is toobtain a $\frac {\gamma m}{2}$-approximation truthful mechanism bygeneralizing a γ-approximation truthful mechanism for twomachines[6]. There is a barrier of 0.75m for this technique due tothe lower bound of 1.5 for two machines. We break this 0.75mbarrier by a new designing technique, rounding a fractionalsolution. We propose a randomized truthful-in-expectation mechanismthat achieves approximation of $\frac{m+5}{2}$, for m machines. For the lower bound side, we focus on an interesting family ofmechanisms, namely task-independent truthful mechanisms.We prove a lower bound of 11/7 for two machines and a lower boundof $\frac{m+1}{2}$ for m machines with respect to thisfamily. They almost match our upper bounds in both cases.

A cost-sharing plan is an arrangement of guidelines characterizing how to distribute the cost among adjusted clients. A cost-sharing strategy is check monotonic in case it satisfies the property that everyone is in a flawless circumstance when the course of action of individuals who get the affiliation creates. CM is a property that passes on a customer's part ought to be more humble when balanced in a more imperative set. CM is an key techniques to achieve the group strategy proofness. By using the multicast plans that objective the enhanced directing, cross-monotonic cost sharing, and stabilize budget. Unsurprising degree cost recuperations is conceivable, and also apply a primal-twofold diagram to in the meantime create an organizing strategy and a cost-sharing course of action, and demonstrate that the subsequent instrument is collect framework proof and ensures off base cost recuperation against a flawless coordinating game plan.

We study the problem of designing truthful mechanisms for makespan minimization in scheduling. In particular, we consider randomized mechanisms for a restriction of the general multi-dimensional domain (i.e., unrelated machines). In a sense, our setting is the simplest multi-dimensional setting, where each machine holds privately only a single-bit of information. Some of the impossibility results for deterministic mechanisms carry over our setting as well. We prove a separation between truthful-in-expectation and universally truthful mechanisms for makespan minimization: We first show how to design an optimal truthful-in-expectation mechanism, and then prove lower bounds on the approximation guarantee of universally truthful mechanisms.

In this work we study mechanisms with verification, as introduced by Nisan and Ronen [STOC 1999], to solve problems involving selfish agents. We provide a technique for designing truthful mechanisms with verification that optimally solve the underlying optimization problem. Problems (optimally) solved with our technique belong to a rich class that includes, as special cases, utilitarian problems and many others considered in literature for so called one-parameter agents (e.g., the make-span). Our technique extends the one recently presented by Auletta et al [ICALP 2006] as it works for any finite multi-dimensional valuation domain. As special case we obtain an alternative technique to optimally solve (though not in polynomial-time) Scheduling Unrelated Machines studied (and solved) by Nisan and Ronen. Interestingly enough, our technique also solves the case of compound agents (i.e., agents declaring more than a value). As an application we provide the first optimal truthful mechanism with verification for Scheduling Unrelated Machines in which every selfish agent controls more than one (unrelated) machine. We also provide methods leading to approximate solutions obtained with polynomial-time truthful mechanisms with verification. With such methods we obtain polynomial-time truthful mechanisms with verification for smooth problems involving compound agents composed by one-parameter valuations. Finally, we investigate the construction of mechanisms (with verification) for infinite domains. We show that existing techniques to obtain truthful mechanisms (for the case in which verification is not allowed), dealing with infinite domains, could completely annul advantages that verification implies.

Approximate composable truthful mechanism design

The connected facility location polytope

Facility location games with distinct desires

A powerful algorithmic technique for truthful mechanism design is the maximal-in-distributional-range (MIDR) paradigm. Unfortunately, many such algorithms use heavy algorithmic machinery, e.g., the...

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.

This research explores integrated and sequential approaches to a combined job scheduling and discrete facility location optimization problem (ScheLoc). The makespan is considered as a criterion for job scheduling. A Tabu Search based Memetic Algorithm (TSMA) has been developed and applied for the former approach due to the NP-hardness of ScheLoc. For the latter approach, the problem is decomposed into two sub-problems m-median and parallel job scheduling with unrelated machines. Extensive numerical tests have confirmed the advantage of the integrated optimization strategy ensured by TSMA in terms of the makespan and the computation time. Conducted computational experiments have also shown the improvement of results generated by TSMA in comparison with another algorithm known from the literature.

The sample average approximation (SAA) approach is a widely used technique, based on Monte‐Carlo simulation, often applied to large‐scale stochastic optimization problems. In this approach, a set of sample average problems with multiple copies of sampled scenarios are generated and solved exactly. In other words, there is an implicit assumption that the sample average problems are solvable to optimality. In some instances, however, the sample average problems might be NP‐hard problems, often difficult or impractical to solve to optimality. In this article, we broaden the scope of the SAA approach and show that even without solving the sample problems to optimality, by combining a heuristic and a lower bounding approach, high‐quality solutions with tight confidence bounds on the optimal solution value can be obtained. We demonstrate this “inexact SAA approach” on two problems. First, we apply it to the Stochastic Connected Facility Location (SConFL) problem, the motivating application for this article, that arises in the design of telecommunications networks. As an additional application, we also use it for the Stochastic Uncapacitated Facility Location (SUFL) problem. Our computational results demonstrate the effectiveness of the inexact SAA approach. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 19–33 2017

Connected facility location via random facility sampling and core detouring