arXiv subjects

Moshe Babaioff

Publications and source records attributed to Moshe Babaioff.

At least 19 recordsLinked to original sources

arXiv2026

Truthful-in-Expectation Mechanisms for MMS Approximation

We study fair allocation of indivisible goods among strategic agents with additive valuations. Motivated by impossibility results for deterministic truthful mechanisms, we focus on randomized mechanisms that are \emph{Truthful-in-Expectation (TIE)}. From a fairness perspective, we seek to guarantee every agent a large fraction of their \emph{Maximin Share (MMS)} ex-post. Among other results, Bu~and~Tao~[FOCS 2025] presented a TIE mechanism that guarantees $\frac{1}{n}$-MMS ex-post. First, we present an ordinal TIE mechanism that guarantees $\frac{1}{H_{n-1} + 2}$-MMS ex-post, where $H_k$ is the $k$-th harmonic number ($H_k \simeq \ln k$). This is nearly best possible for ordinal mechanisms, as even non-truthful ordinal allocation algorithms cannot obtain an approximation better than $\frac{1}{H_n}$. We then show that with just a small amount of additional cardinal information, the ex-post guarantee can be improved to $\Omega(\frac{1}{\log\log n})$-MMS, at the cost of relaxing the incentive requirement to $(1-\varepsilon(n))$-TIE for negligible $\varepsilon(n)$. Finally, for two agents, we present a TIE mechanism that is $\frac{2}{3}$-MMS ex-post. All our mechanisms are ex-ante proportional (thus also providing ``Best-of-Both-Worlds'' results) and run in polynomial time. Moreover, all our results extend to the truncated proportional share (TPS), which is at least as large as the MMS. Our two-agent $\frac{2}{3}$-TPS result is best possible for the TPS.

cs.GT↗

arXiv2026

Approximating Gains-from-Trade in Matching Markets

A central challenge in mechanism design is to develop truthful trade mechanisms that maximize the expected gains-from-trade (GFT) in two-sided markets with strategic agents. As achieving the full GFT is generally impossible, much of the literature has focused on constant-factor approximations. Existing results, however, are limited to the highly structured settings of bilateral trade and double auctions, in which every buyer can trade with every seller. We consider the significantly more general setting of two-sided matching markets with arbitrary downward-closed constraints on the family of allowed matchings. For this setting, we present a simple randomized truthful mechanism that guarantees a constant-factor approximation to the optimal expected GFT. This result also resolves an open problem posed by Cai, Goldner, Ma, and Zhao (2021).

cs.GT↗

arXiv2026

Efficient Interview Scheduling for Stable Matching

The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly interactions such as interviews. We show how to reach interim-stable matchings, under which all matched pairs must have interviewed and agents use expected utilities whenever true values remain unknown, while minimizing both the expected number of interviews and the expected number of interview rounds. We introduce two adaptive algorithms that produce interim-stable matchings: one operates sequentially, and another is a hybrid algorithm that begins by scheduling some interviews in parallel and continues sequentially. Focusing on cases where agents are ex-ante indifferent between agents on the other side, we show that the sequential algorithm performs 2 interviews per agent in expectation. We complement this by showing that any algorithm that performs less than 2 interviews per agent, does not always guarantee interim-stability. We also demonstrate that the hybrid algorithm requires only polylogarithmic expected number of rounds, while still performing only about 2 interviews per agent in expectation. Additionally, the interviews scheduled by our algorithms guarantee an interim-stable matching when Deferred-Acceptance is run after all interviews are completed.

cs.GT↗

arXiv2026

Near-Optimal Best-of-Both-Worlds Fairness for Few Agents

We consider the problem of fair allocation of indivisible goods among agents with additive valuations, aiming for Best-of-Both-Worlds (BoBW) fairness: a distribution over allocations that is ex-ante fair, and additionally, it is supported only on deterministic allocations that are ex-post fair. Existing BoBW algorithms are far from achieving the best possible ex-post fairness guarantees, even in the well studied special case when there are only few agents. We focus on BoBW for few agents, and our main result is the design of the first poly-time BoBW algorithms achieving near-optimal fairness for three agents. We also present optimal poly-time BoBW results for two agents. For three agents, we prove that there exists an ex-ante proportional distribution over at most six allocations, each of which is Epistemic EFX (EEFX) and gives every agent at least $\tfrac{9}{10}$ of her maximin share (MMS). Since MMS allocations need not exist, some agent may fall below her MMS; we guarantee that any such agent is EFX-satisfied -- a new criterion we call "Individually MMS-satisfying or EFX-satisfying (IMMX)". We complement this with an FPTAS preserving all envy-based guarantees, and also preserving all value-based guarantees up to $(1-\varepsilon)$. Furthermore, we present an FPTAS which guarantees exact ex-ante proportionality, while guaranteeing each agent receives $(1-\varepsilon)$ of her MMS or is EFX-satisfied ex-post -- notable, as computing EFX allocations in polynomial time is open even without BoBW constraints. For two agents, we give an FPTAS that is ex-ante envy-free, ex-post EFX, and guarantees each agent $(1-\varepsilon)$ of her MMS, matching the strongest guarantees achievable in polynomial time.

cs.GT↗

arXiv2026

Strengthening Bulow-Klemperer-Style Results for Multi-Unit Auctions

The classic result of Bulow and Klemperer (1996) shows that in multi-unit auctions with $m$ units and $n\geq m$ buyers whose values are sampled i.i.d. from a regular distribution, the revenue of the VCG auction with $m$ additional buyers is at least as large as the optimal revenue. Unfortunately, for regular distributions, adding $m$ additional buyers is sometimes indeed necessary, so the "competition complexity" of the VCG auction is $m$. We seek proving better competition complexity results in two dimensions. First, under stronger distributional assumptions, the competition complexity of VCG auction drops dramatically. In balanced markets (where $m=n$) with MHR distributions, it is sufficient to only add $(e^{1/e} - 1 + o(1))n \approx 0.4447n$ additional buyers to match the optimal revenue -- less than half the number that is necessary under regularity -- and this bound is asymptotically tight. We provide both exact finite-market results for small value of $n$, and closed-form asymptotic formulas for general market with any $m\leq n$, and any target fraction of the optimal revenue. Second, we analyze a supply-limiting variant of VCG auction that caps the number of units sold in a prior-independent way. Whenever the goal is to achieve almost the optimal revenue, this mechanism strictly improves upon standard VCG auction, requiring significantly fewer additional buyers. Together, our results show that both stronger distributional assumptions, as well as a simple prior-independent refinement to the VCG auction, can each substantially reduce the number of additional buyers that is sufficient to achieve (near-)optimal revenue. Our analysis hinges on a unified worst-case reduction to truncated generalized Pareto distributions, enabling both numerical computation and analytical tractability.

cs.GT↗

arXiv2026

Pareto-Efficient Multi-Buyer Mechanisms: Characterization, Fairness and Welfare

A truthful mechanism for a Bayesian single-item auction results with some ex-ante revenue for the seller, and some ex-ante total surplus for the buyers. We study the Pareto frontier of the set of seller-buyers ex-ante utilities, generated by all truthful mechanisms when buyers values are sampled independently and identically (i.i.d.). We first provide a complete structural characterization of the Pareto frontier under natural distributional assumptions. For example, when valuations are drawn i.i.d. from a distribution that is both regular and anti-MHR, every Pareto-optimal mechanism is a second-price auction with a reserve no larger than the monopoly reserve. Building on this, we interpret the problem of picking a mechanism as a two-sided bargaining game, and analyze two canonical Pareto-optimal solutions from cooperative bargaining theory: the Kalai-Smorodinsky (KS) solution, and the Nash solution. We prove that when values are drawn i.i.d. from a distribution that is both regular and anti-MHR, in large markets both solutions yield near-optimal welfare. In contrast, under worst-case MHR distributions, their performance diverges sharply: the KS solution guarantees one-half of the optimal welfare, while the Nash solution might only achieve an arbitrarily small fraction of it. These results highlight the sensitivity of fairness-efficiency tradeoffs to distributional structure, and affirm the KS solution as the more robust notion of fairness for asymmetric two-sided markets.

cs.GT↗

arXiv2026

On Best-of-Both-Worlds Fairness via Sum-of-Variances Minimization

We consider the problem of fairly allocating a set of indivisible goods among agents with additive valuations. Ex-ante fairness (proportionality) can trivially be obtained by giving all goods to a random agent. Yet, such an allocation is very unfair ex-post. This has motivated the Best-of-Both-Worlds (BoBW) approach, seeking a randomized allocation that is ex-ante proportional and is supported only on ex-post fair allocations (e.g., on allocations that are envy-free-up-to-one-good (EF1), or give some constant fraction of the maximin share (MMS)). It is commonly pointed out that the distribution that allocates all goods to one agent at random fails to be ex-post fair as it ignores the variances of the values of the agents. We examine the approach of trying to mitigate this problem by minimizing the sum-of-variances of the values of the agents, subject to ex-ante proportionality. We study the ex-post fairness properties of the resulting distributions. In support of this approach, observe that such an optimization will indeed deterministically output a proportional allocation if such exists. We show that when valuations are identical, this approach indeed guarantees fairness ex-post: all allocations in the support are envy-free-up-to-any-good (EFX), and thus guarantee every agent at least 4/7 of her maximin share (but not her full MMS). On the negative side, we show that this approach completely fails when valuations are not identical: even in the simplest setting of only two agents and two goods, when the additive valuations are not identical, there is positive probability of allocating both goods to the same agent. Thus, the supporting ex-post allocation might not even be EF1, and might not give an agent any constant fraction of her MMS. Finally, we present similar negative results for other natural minimization objectives that are based on variances.

cs.GT↗

arXiv2025

On the Welfare of EIP-1559 with Patient Bidders

The ``EIP-1599 algorithm'' is used by the Ethereum blockchain to assemble transactions into blocks. While prior work has studied it under the assumption that bidders are ``impatient'', we analyze it under the assumption that bidders are ``patient'', which better corresponds to the fact that unscheduled transactions remain in the mempool and can be scheduled at a later time. We show that with ``patient'' bidders, this algorithm produces schedules of near-optimal welfare, provided it is given a mild resource augmentation (that does not increase with the time horizon). We prove some generalizations of the basic theorem, establish lower bounds that rule out several candidate improvements and extensions, and propose several questions for future work.

cs.GT↗

arXiv2025

On the Efficiency of Fair and Truthful Trade Mechanisms

We consider the impact of fairness requirements on the social efficiency of truthful mechanisms for trade, focusing on Bayesian bilateral-trade settings. Unlike the full information case in which all gains-from-trade can be realized and equally split between the two parties, in the private information setting, equitability has devastating welfare implications (even if only required to hold ex-ante). We thus search for an alternative fairness notion and suggest requiring the mechanism to be KS-fair: it must ex-ante equalize the fraction of the ideal utilities of the two traders. We show that there is always a KS-fair (simple) truthful mechanism with expected gains-from-trade that are half the optimum, but always ensuring any better fraction is impossible (even when the seller value is zero). We then restrict our attention to trade settings with a zero-value seller and a buyer with value distribution that is Regular or MHR, proving that much better fractions can be obtained under these conditions.

cs.GT↗

arXiv2024

On Truthful Mechanisms without Pareto-efficiency: Characterizations and Fairness

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.

cs.GT↗

arXiv2024

Bundling in Oligopoly: Revenue Maximization with Single-Item Competitors

We consider a principal seller with $m$ heterogeneous products to sell to an additive buyer over independent items. The principal can offer an arbitrary menu of product bundles, but faces competition from smaller and more agile single-item sellers. The single-item sellers choose their prices after the principal commits to a menu, potentially under-cutting the principal's offerings. We explore to what extent the principal can leverage the ability to bundle product together to extract revenue. Any choice of menu by the principal induces an oligopoly pricing game between the single-item sellers, which may have multiple equilibria. When there is only a single item this model reduces to Bertrand competition, for which the principal's revenue is $0$ at any equilibrium, so we assume that no single item's value is too dominant. We establish an upper bound on the principal's optimal revenue at every equilibrium: the expected welfare after truncating each item's value to its revenue-maximizing price. Under a technical condition on the value distributions -- that the monopolist's revenue is sufficiently sensitive to price -- we show that the principal seller can simply price the grand-bundle and ensure (in any equilibrium) a constant approximation to this bound (and hence to the optimal revenue). We also show that for some value distributions violating our conditions, grand-bundle pricing does not yield a constant approximation to the optimal revenue in any equilibrium.

cs.GT↗

arXiv2024

Share-Based Fairness for Arbitrary Entitlements

We consider the problem of fair allocation of indivisible items to agents that have arbitrary entitlements to the items. Every agent $i$ has a valuation function $v_i$ and an entitlement $b_i$, where entitlements sum up to~1. Which allocation should one choose in situations in which agents fail to agree on one acceptable fairness notion? We study this problem in the case in which each agent focuses on the value she gets, and fairness notions are restricted to be {\em share based}. A {\em share} $s$ is an function that maps every $(v_i,b_i)$ to a value $s(v_i,b_i)$, representing the minimal value $i$ should get, and $s$ is {\em feasible} if it is always possible to give every agent $i$ value of at least $s(v_i,b_i)$. Our main result is that for additive valuations over goods there is an allocation that gives every agent at least half her share value, regardless of which feasible share-based fairness notion the agent wishes to use. Moreover, the ratio of half is best possible. More generally, we provide tight characterizations of what can be achieved, both ex-post (as single allocations) and ex-ante (as expected values of distributions of allocations), both for goods and for chores. We also show that for chores one can achieve the ex-ante and ex-post guarantees simultaneously (a ``best of both world" result), whereas for goods one cannot.

cs.GT↗

arXiv2024

Learning to Maximize Gains From Trade in Small Markets

We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an unknown distribution from which we are given a polynomial number of samples. Our first result is a general impossibility for the case of correlated distributions of values even between just one seller and two buyers, in contrast to the case of one seller and one buyer (bilateral trade) where this is possible. Our second result is an efficient learning algorithm for one seller and two buyers in the case of independent distributions which is based on a novel algorithm for computing optimal mechanisms for finitely supported and explicitly given independent distributions. Both results rely heavily on characterizations of (dominant-strategy) incentive compatible mechanisms that are strongly budget-balanced.

cs.GT↗

arXiv2023

On the Computational Complexity of Mechanism Design in Single-Crossing Settings

We explore the performance of polynomial-time incentive-compatible mechanisms in single-crossing domains. Single-crossing domains were extensively studied in the economics literature. Roughly speaking, a domain is single crossing if monotonicity characterizes incentive compatibility. That is, single-crossing domains are the standard mathematical formulation of domains that are informally known as ``single parameter''. In all major single-crossing domains studied so far (e.g., welfare maximization in various auctions with single-minded bidders, makespan minimization on related machines), the performance of the best polynomial-time incentive-compatible mechanisms matches the performance of the best polynomial-time non-incentive-compatible algorithms. Our two main results make progress in understanding the power of incentive-compatible polynomial-time mechanisms in single-crossing domains: We provide the first proof of a gap in the power of polynomial-time incentive-compatible mechanisms and polynomial-time non-incentive-compatible algorithms: we present an objective function in a single-crossing multi-unit auction for which there is a polynomial-time algorithm that provides an approximation ratio of $\frac{1}{2}$, yet no polynomial-time incentive-compatible mechanism provides a finite approximation (under standard computational complexity assumptions). The objective function used above is not natural. We show that to some extent this is unavoidable by providing a sweeping positive result for the most natural objective function in multi-unit auctions, that of welfare maximization. We present an incentive-compatible FPTAS mechanism for every multi-unit auction with single-crossing domains. This improves over the mechanism of Briest et al. [STOC'05] that only applies to the much simpler case of single-minded bidders.

cs.GT↗

arXiv2022

Simplicity in Auctions Revisited: The Primitive Complexity

In this paper we revisit the notion of simplicity in mechanisms. We consider a seller of $m$ items, facing a single buyer with valuation $v$. We observe that previous attempts to define complexity measures often fail to classify mechanisms that are intuitively considered simple (e.g., the "selling separately" mechanism) as such. We suggest to view a menu as simple if a bundle that maximizes the buyer's profit can be found by conducting a few primitive operations that are considered simple. The \emph{primitive complexity of a menu} is the number of primitive operations needed to (adaptively) find a profit-maximizing entry in the menu. In this paper, the primitive operation that we study is essentially computing the outcome of the "selling separately" mechanism. Does the primitive complexity capture the simplicity of other auctions that are intuitively simple? We consider \emph{bundle-size pricing}, a common pricing method in which the price of a bundle depends only on its size. Our main technical contribution is determining the primitive complexity of bundle-size pricing menus in various settings. We show that for any distribution $\cal D$ over weighted matroid rank valuations, even distributions with arbitrary correlation among their values, there is always a bundle-size pricing menu with low primitive complexity that achieves almost the same revenue as the optimal bundle-size pricing menu. As part of this proof we provide a randomized algorithm that for any weighted matroid rank valuation $v$ and integer $k$, finds the most valuable set of size $k$ with only a poly-logarithmic number of demand and value queries. We show that this result is essentially tight in several aspects. For example, if the valuation $v$ is submodular, then finding the most valuable set of size $k$ requires exponentially many queries (this solves an open question of Badanidiyuru et al. [EC'12]).

cs.GT↗

arXiv2022

Fair Shares: Feasibility, Domination and Incentives

We consider fair allocation of a set $M$ of indivisible goods to $n$ equally-entitled agents, with no monetary transfers. Every agent $i$ has a valuation $v_i$ from some given class of valuation functions. A share $s$ is a function that maps a pair $(v_i,n)$ to a value, with the interpretation that if an allocation of $M$ to $n$ agents fails to give agent $i$ a bundle of value at least equal to $s(v_i,n)$, this serves as evidence that the allocation is not fair towards $i$. For such an interpretation to make sense, we would like the share to be feasible, meaning that for any valuations in the class, there is an allocation that gives every agent at least her share. The maximin share was a natural candidate for a feasible share for additive valuations. However, Kurokawa, Procaccia and Wang [2018] show that it is not feasible. We initiate a systematic study of the family of feasible shares. We say that a share is \emph{self maximizing} if truth-telling maximizes the implied guarantee. We show that every feasible share is dominated by some self-maximizing and feasible share. We seek to identify those self-maximizing feasible shares that are polynomial time computable, and offer the highest share values. We show that a SM-dominating feasible share -- one that dominates every self-maximizing (SM) feasible share -- does not exist for additive valuations (and beyond). Consequently, we relax the domination property to that of domination up to a multiplicative factor of $\rho$ (called $\rho$-dominating). For additive valuations we present shares that are feasible, self-maximizing and polynomial-time computable. For $n$ agents we present such a share that is $\frac{2n}{3n-1}$-dominating. For two agents we present such a share that is $(1 - \epsilon)$-dominating. Moreover, for these shares we present poly-time algorithms that compute allocations that give every agent at least her share.

econ.TH↗

arXiv2022

Truthful Online Scheduling of Cloud Workloads under Uncertainty

Cloud computing customers often submit repeating jobs and computation pipelines on \emph{approximately} regular schedules, with arrival and running times that exhibit variance. This pattern, typical of training tasks in machine learning, allows customers to partially predict future job requirements. We develop a model of cloud computing platforms that receive statements of work (SoWs) in an online fashion. The SoWs describe future jobs whose arrival times and durations are probabilistic, and whose utility to the submitting agents declines with completion time. The arrival and duration distributions, as well as the utility functions, are considered private customer information and are reported by strategic agents to a scheduler that is optimizing for social welfare. We design pricing, scheduling, and eviction mechanisms that incentivize truthful reporting of SoWs. An important challenge is maintaining incentives despite the possibility of the platform becoming saturated. We introduce a framework to reduce scheduling under uncertainty to a relaxed scheduling problem without uncertainty. Using this framework, we tackle both adversarial and stochastic submissions of statements of work, and obtain logarithmic and constant competitive mechanisms, respectively.

cs.GT↗

arXiv2021

A Note on the Gains from Trade of the Random-Offerer Mechanism

We study the classic bilateral trade setting. Myerson and Satterthwaite show that there is no Bayesian incentive compatible and budget-balanced mechanism that obtains the gains from trade of the first-best mechanism. Consider the random-offerer mechanism: with probability $\frac{1}{2}$ run the \emph{seller-offering} mechanism, in which the seller offers the buyer a take-it-or-leave-it price that maximizes the expected profit of the seller, and with probability $\frac{1}{2}$ run the \emph{buyer-offering} mechanism. Very recently, Deng, Mao, Sivan, and Wang showed that the gains from trade of the random-offerer mechanism is at least a constant factor of $\frac 1 {8.23}\approx 0.121$ of the gains from trade of the first best mechanism. Perhaps a natural conjecture is that the gains-from-trade of the random-offerer mechanism, which is known to be at least half of the gains-from-trade of the second-best mechanism, is also at least half of the gains-from-trade of the first-best mechanism. However, in this note we exhibit distributions such as the gains-from trade of the random-offerer mechanism is smaller than a $0.495$-fraction of the gains-from-trade of the first-best mechanism.

cs.GT↗