We consider the problem of allocating a set on indivisible items to players with private preferences in an efficient and fair way. We focus on valuations that have dichotomous marginals, in which the added value of any item to a set is either 0 or 1, and aim to design truthful allocation mechanisms (without money) that maximize welfare and are fair. For the case that players have submodular valuations with dichotomous marginals, we design such a deterministic truthful allocation mechanism. The allocation output by our mechanism is Lorenz dominating, and consequently satisfies many desired fairness properties, such as being envy-free up to any item (EFX), and maximizing the Nash Social Welfare (NSW). We then show that our mechanism with random priorities is envy-free ex-ante, while having all the above properties ex-post. Furthermore, we present several impossibility results precluding similar results for the larger class of XOS valuations.
To gauge the robustness of our positive results, we also study $ε$-dichotomous valuations, in which the added value of any item to a set is either non-positive, or in the range $[1, 1 + ε]$. We show several impossibility results in this setting, and also a positive result: for players that have additive $ε$-dichotomous valuations with sufficiently small $ε$, we design a randomized truthful mechanism with strong ex-post guarantees. For $ρ= \frac{1}{1 + ε}$, the allocations that it produces generate at least a $ρ$-fraction of the maximum welfare, and enjoy $ρ$-approximations for various fairness properties, such as being envy-free up to one item (EF1), and giving each player at least her maximin share.
We study the problem of allocating indivisible goods among agents in a fair manner. While envy-free allocations of indivisible goods are not guaranteed to exist, envy-freeness can be achieved by additionally providing some subsidy to the agents. These subsidies can be alternatively viewed as a divisible good (money) that is fractionally assigned among the agents to realize an envy-free outcome. In this setup, we bound the subsidy required to attain envy-freeness among agents with dichotomous valuations, i.e., among agents whose marginal value for any good is either zero or one. We prove that, …
We study the problem of allocating indivisible goods among strategic agents. We focus on settings wherein monetary transfers are not available and each agent's private valuation is a submodular function with binary marginals, i.e., the agents' valuations are matroid-rank functions. In this setup, we establish a notable dichotomy between two of the most well-studied fairness notions in discrete fair division; specifically, between envy-freeness up to one good (EF1) and maximin shares (MMS). First, we show that a Pareto-efficient mechanism of Babaioff et al. (2021) is group strategy-proof for fi…
We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides $m^{\frac 1 2 -ε}$ approximation to the social welfare and uses value queries only must use exponentially many value queries, where $m$ is the number of items. In contrast, ignoring incentives there exist constant ratio approximation algorithms for this problem. Our approach is based on a novel \emph{direct hardness} approach and completely skips the notoriously hard characterization step. The characterization step was the main obstacle for proving impossibility resu…
Submodular over signal (SOS) defines a family of interesting functions for which there exist truthful mechanisms with constant approximation to the social welfare for agents with interdependent valuations. The best-known truthful auction is of $4$-approximation and a lower bound of 2 was proved. We propose a new and simple truthful mechanism to achieve an approximation ratio of 3.315.
One of the fundamental questions of Algorithmic Mechanism Design is whether there exists an inherent clash between truthfulness and computational tractability: in particular, whether polynomial-time truthful mechanisms for combinatorial auctions are provably weaker in terms of approximation ratio than non-truthful ones. This question was very recently answered for universally truthful mechanisms for combinatorial auctions \cite{D11}, and even for truthful-in-expectation mechanisms \cite{DughmiV11}. However, both of these results are based on information-theoretic arguments for valuations given…
We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with {\em dichotomous preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are particularly interested in the well-known {\em Random Serial Dictatorship} mechanism. For dichotomous preferences, we first show that truthful, symmetric and optimal mechanisms exist if intractable mechanisms are allowed. We then provide a connection to online bipartite matching. Using this connection, it is possible to design truthful, symmetric and tractable mechanisms that …
In markets such as digital advertising auctions, bidders want to maximize value rather than payoff. This is different to the utility functions typically assumed in auction theory and leads to different strategies and outcomes. We refer to bidders who maximize value as value bidders. While simple single-object auction formats are truthful, standard multi-object auction formats allow for manipulation. It is straightforward to show that there cannot be a truthful and revenue-maximizing deterministic auction mechanism with value bidders and general valuations. Approximation has been used as a mean…
We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation in order to receive a better allocation. A (direct-revelation) mechanism takes agents' reported valuations as input and outputs an allocation that satisfies a given fairness requirement. A natural and fundamental open problem, first raised by [Chen et al., 2010] and subsequently raised by [Procaccia, 2013] [Aziz and Ye, 2014] [Branzei and Miltersen, 2015] [Menon and Larson, 2017] [Bei et al., 2017] [Bei et al., 2020]…
In a seminal paper, McAfee (1992) presented a truthful mechanism for double auctions, attaining asymptotically-optimal gain-from-trade without any prior information on the valuations of the traders. McAfee's mechanism handles single-parametric agents, allowing each seller to sell a single unit and each buyer to buy a single unit. This paper presents a double-auction mechanism that handles multi-parametric agents and allows multiple units per trader, as long as the valuation functions of all traders have decreasing marginal returns. The mechanism is prior-free, ex-post individually-rational, do…
We consider the problem of designing truthful auctions, when the bidders' valuations have a public and a private component. In particular, we consider combinatorial auctions where the valuation of an agent $i$ for a set $S$ of items can be expressed as $v_if(S)$, where $v_i$ is a private single parameter of the agent, and the function $f$ is publicly known. Our motivation behind studying this problem is two-fold: (a) Such valuation functions arise naturally in the case of ad-slots in broadcast media such as Television and Radio. For an ad shown in a set $S$ of ad-slots, $f(S)$ is, say, the num…
The notion of \emph{envy-freeness} is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are unfortunately not guaranteed to exist. Classical works have avoided this issue by introducing an additional divisible resource, i.e., money, to subsidize envious agents. In this paper, we aim to design a truthful allocation mechanism of indivisible goods to achieve both fairness and efficiency criteria with a limited amount of subsidy. Following the work of Halpern and Shah, our central question is as follows: to what extent do we need to …
The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Under truthful bidding, the SMRA is known to output a Walrasian equilibrium that maximizes social welfare provided the bidder valuation functions satisfy the gross substitutes property. Recently, it was shown that the combinatorial clock auction (CCA) provides good welfare guarantees for general classes of valuation functions. This motivates the question of whether similar welfare guarantees hold for the SMRA in the case of general valuation functions.…
If a two-player social welfare maximization problem does not admit a PTAS, we prove that any maximal-in-range truthful mechanism that runs in polynomial time cannot achieve an approximation factor better than 1/2. Moreover, for the k-player version of the same problem, the hardness of approximation improves to 1/k under the same two-player hardness assumption. (We note that 1/k is achievable by a trivial deterministic maximal-in-range mechanism.) This hardness result encompasses not only deterministic maximal-in-range mechanisms, but also all universally-truthful randomized maximal in range al…
The focus of classic mechanism design has been on truthful direct-revelation mechanisms. In the context of combinatorial auctions the truthful direct-revelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrict…
We consider a ridesharing problem where there is uncertainty about the completion of trips from both drivers and riders. Specifically, we study ridesharing mechanisms that aim to incentivize commuters to reveal their valuation for trips and their probability of undertaking their trips. Due to the interdependence created by the uncertainty on commuters' valuations, we show that the Groves mechanisms are not ex-post truthful even if there is only one commuter whose valuation depends on the other commuters' uncertainty of undertaking their trips. To circumvent this impossibility, we propose an ex…
We consider an infinite horizon dynamic mechanism design problem with interdependent valuations. In this setting the type of each agent is assumed to be evolving according to a first order Markov process and is independent of the types of other agents. However, the valuation of an agent can depend on the types of other agents, which makes the problem fall into an interdependent valuation setting. Designing truthful mechanisms in this setting is non-trivial in view of an impossibility result which says that for interdependent valuations, any efficient and ex-post incentive compatible mechanism …
We study procurement games where each seller supplies multiple units of his item, with a cost per unit known only to him. The buyer can purchase any number of units from each seller, values different combinations of the items differently, and has a budget for his total payment. For a special class of procurement games, the {\em bounded knapsack} problem, we show that no universally truthful budget-feasible mechanism can approximate the optimal value of the buyer within $\ln n$, where $n$ is the total number of units of all items available. We then construct a polynomial-time mechanism that giv…
Complements between goods - where one good takes on added value in the presence of another - have been a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications for combinatorial auctions, like spectrum license auctions. On the other, welfare maximization in the presence of complements is notoriously difficult, and this intractability has stymied theoretical progress in the area. For example, there are no known positive results for combinatorial auctions in which bidder valuations are multi-parameter and non-compleme…
We prove new positive and negative results concerning the existence of truthful and individually rational mechanisms for purchasing private data from individuals with unbounded and sensitive privacy preferences. We strengthen the impossibility results of Ghosh and Roth (EC 2011) by extending it to a much wider class of privacy valuations. In particular, these include privacy valuations that are based on (ε, δ)-differentially private mechanisms for non-zero δ, ones where the privacy costs are measured in a per-database manner (rather than taking the worst case), and ones that do not depend on t…
We propose a mechanism to allocate slots fairly at congested airports. This mechanism: (a) ensures that the slots are allocated according to the true valuations of airlines, (b) provides fair opportunities to the flights connecting remote cities to large airports, and (c) controls the number of flights in each slot to minimize congestion. The mechanism draws inspiration from economic theory. It allocates the slots based on an affine maximizer allocation rule and charges payments to the airlines such that they are incentivized to reveal their true valuations. The allocation also optimizes the o…
We revisit the classic problem of fair division from a mechanism design perspective, using {\em Proportional Fairness} as a benchmark. In particular, we aim to allocate a collection of divisible items to a set of agents while incentivizing the agents to be truthful in reporting their valuations. For the very large class of homogeneous valuations, we design a truthful mechanism that provides {\em every agent} with at least a $1/e\approx 0.368$ fraction of her Proportionally Fair valuation. To complement this result, we show that no truthful mechanism can guarantee more than a $0.5$ fraction, ev…
We study incentive compatible mechanisms for Combinatorial Auctions where the bidders have submodular (or XOS) valuations and are budget-constrained. Our objective is to maximize the \emph{liquid welfare}, a notion of efficiency for budget-constrained bidders introduced by Dobzinski and Paes Leme (2014). We show that some of the known truthful mechanisms that best-approximate the social welfare for Combinatorial Auctions with submodular bidders through demand query oracles can be adapted, so that they retain truthfulness and achieve asymptotically the same approximation guarantees for the liqu…
Fairness is well studied in the context of resource allocation. Researchers have proposed various fairness notions like envy-freeness (EF), and its relaxations, proportionality and max-min share (MMS). There is vast literature on the existential and computational aspects of such notions. While computing fair allocations, any algorithm assumes agents' truthful reporting of their valuations towards the resources. Whereas in real-world web-based applications for fair division, the agents involved are strategic and may manipulate for individual utility gain. In this paper, we study strategy-proof …
Sponsored search auctions constitute one of the most successful applications of microeconomic mechanisms. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and to assure both the advertisers and the auctioneer a non-negative utility. Nonetheless, in sponsored search auctions, the click-through-rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard truthful mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the cri…
Recently, a randomized mechanism has been discovered [Dughmi, Roughgarden and Yan; STOC'11] for combinatorial auctions that is truthful in expectation and guarantees a (1-1/e)-approximation to the optimal social welfare when players have coverage valuations. This approximation ratio is the best possible even for non-truthful algorithms, assuming $P \neq NP$. Given the recent sequence of negative results for combinatorial auctions under more restrictive notions of incentive compatibility, this development raises a natural question: Are truthful-in-expectation mechanisms compatible with polynomi…
Budget feasible mechanism design studies procurement combinatorial auctions where the sellers have private costs to produce items, and the buyer(auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint on the total payment. One of the most important questions in the field is "which valuation domains admit truthful budget feasible mechanisms with `small' approximations (compared to the social optimum)?" Singer showed that additive and submodular functions have such constant approximations. Recently, Dobzinski, Papadimitriou, and Singer gave an O(…
Interdependent values make basic auction design tasks -- in particular maximizing welfare truthfully in single-item auctions -- quite challenging. Eden et al. recently established that if the bidders valuation functions are submodular over their signals (a.k.a. SOS), a truthful 4-approximation to the optimal welfare exists. We show existence of a mechanism that is truthful and achieves a tight 2-approximation to the optimal welfare when signals are binary. Our mechanism is randomized and assigns bidders only 0 or 0.5 probabilities of winning the item. Our results utilize properties of submodul…
We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise …
This manuscript presents an alternative implementation of the truthful-in-expectation mechanism of Dughmi, Roughgarden and Yan for combinatorial auctions with weighted-matroid-rank-sum valuations. The new implementation uses only value queries and is approximately truthful-in-expectation, in the sense that by reporting truthfully each agent maximizes his utility within a multiplicative 1-o(1) factor. It still provides an optimal (1-1/e-o(1))-approximation in social welfare. We achieve this by first presenting an approximately maximal-in-distributional-range allocation rule and then showing a b…
We characterize the communication complexity of truthful mechanisms. Our departure point is the well known taxation principle. The taxation principle asserts that every truthful mechanism can be interpreted as follows: every player is presented with a menu that consists of a price for each bundle (the prices depend only on the valuations of the other players). Each player is allocated a bundle that maximizes his profit according to this menu. We define the taxation complexity of a truthful mechanism to be the logarithm of the maximum number of menus that may be presented to a player. Our main …
We consider a cost sharing problem on a weighted undirected graph, where all the nodes want to connect to a special node called source, and they need to share the total cost (weights) of the used edges. Each node except for the source has a private valuation of the connection, and it may block others' connections by strategically cutting its adjacent edges to reduce its cost share, which may increase the total cost. We aim to design mechanisms to prevent the nodes from misreporting their valuations and cutting their adjacent edges. We first show that it is impossible for such a mechanism to fu…
Scheduling on related machines ($Q||C_{\max}$) is one of the most important problems in the field of Algorithmic Mechanism Design. Each machine is controlled by a selfish agent and her valuation can be expressed via a single parameter, her {\em speed}. In contrast to other similar problems, Archer and Tardos \cite{AT01} showed that an algorithm that minimizes the makespan can be truthfully implemented, although in exponential time. On the other hand, if we leave out the game-theoretic issues, the complexity of the problem has been completely settled -- the problem is strongly NP-hard, while th…
We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation for two buyers with XOS valuations over $m$ items requires $\exp(Ω(\varepsilon^2 \cdot m))$ communication, whereas a non-truthful algorithm by Dobzinski and Schapira [SODA 2006] and Feige [2009] is already known to achieve a $\frac{3}{4}$-approximation in $poly(m)$ communication. We obtain our separation by proving that…
A seminal theorem of Myerson and Satterthwaite (1983) proves that, in a game of bilateral trade between a single buyer and a single seller, no mechanism can be simultaneously individually-rational, budget-balanced, incentive-compatible and socially-efficient. However, the impossibility disappears if the price is fixed exogenously and the social-efficiency goal is subject to individual-rationality at the given price. We show that the impossibility comes back if there are multiple units of the same good, or multiple types of goods, even when the prices are fixed exogenously. Particularly, if the…
We consider the problem of designing a revenue-maximizing auction for a single item, when the values of the bidders are drawn from a correlated distribution. We observe that there exists an algorithm that finds the optimal randomized mechanism that runs in time polynomial in the size of the support. We leverage this result to show that in the oracle model introduced by Ronen and Saberi [FOCS'02], there exists a polynomial time truthful in expectation mechanism that provides a $(\frac 3 2+ε)$-approximation to the revenue achievable by an optimal truthful-in-expectation mechanism, and a polynomi…
Motivated by applications such as stock exchanges and spectrum auctions, there is a growing interest in mechanisms for arranging trade in two-sided markets. Existing mechanisms are either not truthful, or do not guarantee an asymptotically-optimal gain-from-trade, or rely on a prior on the traders' valuations, or operate in limited settings such as a single kind of good. We extend the random market-halving technique used in earlier works to markets with multiple kinds of goods, where traders have gross-substitute valuations. We present MIDA: a Multi Item-kind Double-Auction mechanism. It is pr…
We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of $O(\log^2 m)$ [STOC'06], where $m$ is the number of items. This was subsequently improved to $O(\log m\log \log m)$ [Dobzinski, APPROX'07] and then to $O(\log m)$ [Krysta and Vocking, ICALP'12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an a…
We consider players that have very limited knowledge about their own valuations. Specifically, the only information that a Knightian player $i$ has about the profile of true valuations, $θ^*$, consists of a set of distributions, from one of which $θ_i^*$ has been drawn. We prove a ``robustness'' theorem for Knightian players in single-parameter domains: every mechanism that is weakly dominant-strategy truthful for classical players continues to be well-behaved for Knightian players that choose undominated strategies.
We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on the case of two players with additive valuation functions and our purpose is twofold. First, our main result provides a complete characterization of truthful mechanisms that allocate all the items to the players. Our characterization reveals an interesting structure underlying all truthful mechanisms, showing that they can be decomposed into two components: a…
We design an expected polynomial-time, truthful-in-expectation, (1-1/e)-approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are m matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage functions, matroid weighted-rank functions, and convex combinations thereof. Our approximation factor is the best possible, even for known and explicitly given coverage valuations, assuming P != NP. Ours is the first truthful-in-expectation …
We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -- maximum Nash welfare (MNW) -- provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNW -- known to be group strategyproof, envy-free, and Pareto op…
With the rapidly growing demand for the cloud services, a need for efficient methods to trade computing resources increases. Commonly used fixed-price model is not always the best approach for trading cloud resources, because of its inflexible and static nature. Dynamic trading systems, which make use of market mechanisms, show promise for more efficient resource allocation and pricing in the cloud. However, most of the existing mechanisms ignore the seller's costs of providing the resources. In order to address it, we propose a single-sided market mechanism for trading virtual machine instanc…
We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources or services from a set of agents. Ideally, the auctioneer would like to select a subset of the resources so as to maximize his valuation function, without exceeding a given budget. As the resources are owned by strategic agents however, our overall goal is to design mechanisms that are truthful, budget-feasible, and obtain a good approximation to the optimal value. Budget-feasibility creates additional challenges, making several approaches inapplicable in this setting. Previ…
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, …
