Carmine Ventre

More powerful and simpler cost-sharing methods

We provide a new technique to derive group strategyproof mechanisms for the cost-sharing problem. Our technique is simpler and provably more powerful than the existing one based on so called cross-monotonic cost-sharing methods given by Moulin and Shenker [1997]. Indeed, our method yields the first polynomial-time mechanism for the Steiner tree game which is group strategyproof, budget balance and also meets other standard requirements (No Positive Transfer, Voluntary Participation and Consumer Sovereignty). A known result by Megiddo [1978] implies that this result cannot be achieved with cross-monotonic cost-sharing methods, even if using exponential-time mechanisms.

Sharing the Cost of Multicast Transmissions in Wireless Networks

We investigate the problem of sharing the cost of a multicast transmission in a wireless network where each node (radio station) of the network corresponds to (a set of) user(s) potentially interested in receiving the transmission. As in the model considered by Feigenbaum et al [2001], users may act selfishly and report a false ”level of interest” in receiving the transmission trying to be charged less by the system. We consider the issue of designing a so called truthful mechanisms for the problem of maximizing the net worth (i.e., the overall ”happiness” of the users minus the cost of the transmission) for the case of wireless networks. Intuitively, truthful mechanism guarantee that no user has an incentive in reporting a false valuation of the transmission. Unlike the ”wired” network case, here the cost of a set of connections implementing a multicast tree is not the sum of the single edge costs, thus introducing a complicating factor in the problem. We provide both positive and negative results on the existence of optimal algorithms for the problem and their use to obtain VCG truthful mechanisms achieving the same performances.

Combinatorial auctions with verification are tractable

We study mechanism design for social welfare maximization in combinatorial auctions with general bidders given by demand oracles. It is a major open problem in this setting to design a deterministic truthful auction which would provide the best possible approximation guarantee in polynomial time, even if bidders are double-minded (i.e., they assign positive value to only two sets in their demand collection). On the other hand, there are known such randomized truthful auctions in this setting. In the general model of verification (i.e., some kind of overbidding can be detected) we design the first deterministic truthful auctions which indeed provide essentially the best possible approximation guarantees achievable by any polynomial-time algorithm. This shows that deterministic truthful auctions have the same power as randomized ones if the bidders withdraw from unrealistic lies.

Mechanisms for multi-unit combinatorial auctions with a few distinct goods

We design and analyze deterministic truthful approximation mechanisms for multi-unit Combinatorial Auctions with only a constant number of distinct goods, each in arbitrary limited supply. Prospective buyers (bidders) have preferences over multisets of items, i.e. for more than one unit per distinct good. Our objective is to determine allocations of multisets that maximize the Social Welfare. Despite the recent theoretical advances on the design of truthful Combinatorial Auctions (for several distinct goods) and multi-unit auctions (for a single good), results for the combined setting are much scarser. Our main results are for multi-minded and submodular bidders. In the first setting each bidder has a positive value for being allocated one multiset from a prespecified demand set of alternatives. In the second setting each bidder is associated to a submodular valuation function that defines his value for the multiset he is allocated. For multi-minded bidders we design a truthful FPTAS that fully optimizes the Social Welfare, while violating the supply constraints on goods within factor (1+e) for any fixed e > 0 (i.e., the approximation applies to the constraints and not to the Social Welfare). This result is best possible, in that full optimization is impossible without violating the supply constraints. It also improves significantly upon a related result of Grandoni et al. [SODA 2010]. For submodular bidders we extend a general technique by Dobzinski and Nisan [JAIR, 2010] for multi-unit auctions, to the case of multiple distinct goods. We use this extension to obtain a PTAS that approximates the optimum Social Welfare within factor (1+e) for any fixed e > 0, without violating the supply constraints. This result is best possible as well. Our allocation algorithms are Maximum-in-Range and yield truthful mechanisms when paired with Vickrey-Clarke-Groves payments.

Combinatorial auctions without money

Algorithmic Mechanism Design attempts to marry computation and incentives, mainly by leveraging monetary transfers between designer and selfish agents involved. This is principally because in absence of money, very little can be done to enforce truthfulness. However, in certain applications, money is unavailable, morally unacceptable or might simply be at odds with the objective of the mechanism. For example, in combinatorial auctions (CAs), the paradigmatic problem of the area, we aim at solutions of maximum social welfare but still charge the society to ensure truthfulness. Additionally, truthfulness of CAs is poorly understood already in the case in which bidders happen to be interested in only two different sets of goods. We focus on the design of incentive-compatible CAs without money in the general setting of k-minded bidders. We trade monetary transfers with the observation that the mechanism can detect certain lies of the bidders: i.e., we study truthful CAs with verification and without money. We prove a characterization of truthful mechanisms, which makes an interesting parallel with the well-understood case of CAs with money for single-minded bidders. We then give a host of upper bounds on the approximation ratio obtained by either deterministic or randomized truthful mechanisms when the sets and valuations are private knowledge of the bidders. (Most of these mechanisms run in polynomial time and return solutions with (nearly) best possible approximation guarantees.) We complement these positive results with a number of lower bounds (some of which are essentially tight) that hold in the easier case of public sets. We thus provide an almost complete picture of truthfully approximating CAs in this general setting with multi-dimensional bidders.

Optimal collusion-resistant mechanisms with verification

We present the first general positive result on the construction of collusion-resistant mechanisms, that is, mechanisms that guarantee dominant strategies even when agents can form arbitrary coalitions and exchange compensations (sometimes referred to as transferable utilities or side payments). This is a much stronger solution concept as compared to truthful or even group strategyproof mechanisms, and only impossibility results were known for this type of mechanisms in the “classical” model.

On Stackelberg Pricing with Computationally Bounded Consumers

In a Stackelberg pricing game a leader aims to set prices on a subset of a given collection of items, such as to maximize her revenue from a follower purchasing a feasible subset of the items. We focus on the case of computationally bounded followers who cannot optimize exactly over the range of all feasible subsets, but apply some publicly known algorithm to determine the set of items to purchase. This corresponds to general multi-dimensional pricing assuming that consumers cannot optimize over the full domain of their valuation functions but still aim to act rationally to the best of their ability. We consider two versions of this novel type of Stackelberg pricing games. Assuming that items are weighted objects and the follower seeks to purchase a min-cost selection of objects of some minimum weight (the Min-Knapsack problem) and uses a simple greedy 2-approximate algorithm, we show how an extension of the known single-price algorithm can be used to derive a polynomial-time (2 + ?)-approximation algorithm for the leaders revenue maximization problem based on so-called near-uniform price assignments. We also prove the problem to be strongly NP-hard. Considering the case that items are subsets of some ground set which the follower seeks to cover (the Set-Cover problem) via a standard primal-dual approach, we prove that near-uniform price assignments fail to yield a good approximation guarantee. However, in the special case of elements with frequency 2 (the Vertex-Cover problem) it turns out that exact revenue maximization can be done in polynomial-time. This stands in sharp contrast to the fact that revenue maximization becomes APX-hard already for elements with frequency 3.

New constructions of mechanisms with verification

A social choice function A is implementable with verification if there exists a payment scheme P such that (A,P) is a truthful mechanism for verifiable agents [Nisan and Ronen, STOC 99]. We give a simple sufficient condition for a social choice function to be implementable with verification for comparable types. Comparable types are a generalization of the well-studied one-parameter agents. Based on this characterization, we show that a large class of objective functions μ admit social choice functions that are implementable with verification and minimize (or maximize) μ. We then focus on the well-studied case of one-parameter agents. We give a general technique for constructing efficiently computable social choice functions that minimize or approximately minimize objective functions that are non-increasing and neutral (these are functions that do not depend on the valuations of agents that have no work assigned to them). As a corollary we obtain efficient online and offline mechanisms with verification for some hard scheduling problems on related machines.

Free-riders in steiner tree cost-sharing games

We consider cost-sharing mechanisms for the Steiner tree game. In this well-studied cooperative game, each selfish user expresses his/her willingness to pay for being connected to a source node s in an underlying graph. A mechanism decides which users will be connected and divides the cost of the corresponding (optimal) Steiner tree among these users (budget balance condition). Since users can form coalitions and misreport their willingness to pay, the mechanism must be group strategyproof: even coalitions of users cannot benefit from lying to the mechanism. We present new polynomial-time mechanisms which satisfy a standard set of axioms considered in the literature (i.e., budget balance, group strategyproofness, voluntary participation, consumer sovereignty, no positive transfer, cost optimality) and consider the free riders issue recently raised by Immorlica et al. [SODA 2005]: it would be desirable to avoid users that are connected for free. We also provide a number of negative results on the existence of polynomial-time mechanisms with certain guarantee on the number of free riders. Finally, we extend our technique and results to a variant considered by Bilo et al. [SPAA 2004] with applications to wireless multicast cost sharing.

On stackelberg pricing with computationally bounded customers

In Stackelberg pricing a leader sets prices for items to maximize revenue from a follower purchasing a feasible subset of items. We consider computationally bounded followers who cannot optimize exactly over the range of all feasible subsets, but who apply publicly known algorithms to determine the items to purchase. This corresponds to general multidimensional pricing when customers cannot optimize their valuation functions efficiently but still aim to act rationally to the best of their ability. We consider two versions of this novel type of pricing problem. In the MIn-KNAPSACK variant items are weighted objects and the follower seeks to purchase a min-cost selection of objects of some bounded weight. When he uses a greedy 2-approximation algorithm, we provide a polynomial-time (2+e) -approximation algorithm for the leaders revenue maximization problem based on so-called near-uniform price assignments. We also prove the problem to be strongly NP-hard. In the SET-COVER variant items are subsets of some ground set which the follower seeks to cover. When he uses a standard primal-dual approach, we prove that exact revenue maximization is possible in polynomial time when elements have frequency 2 (VERTEX-COVER variant). This stands in sharp contrast to APX-hardness for the problem with elements of frequency 3.