Moshe Babaioff

Moshe Babaioff, Uriel Feige

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 $ρ$ (called $ρ$-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 $(1 - ε)$-dominating. Moreover, for these shares we present poly-time algorithms that compute allocations that give every agent at least her share.

Moshe Babaioff, Noam Nisan

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.

Moshe Babaioff, Noam Manaker Morag

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.

Moshe Babaioff, Uriel Feige, Noam Manaker Morag

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 $\frac{1}{H_n + 2}$-MMS ex-post, where $H_n$ is the $n$-th harmonic number ($H_n \simeq \ln n$). 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 $Ω(\frac{1}{\log\log n})$-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.

Moshe Babaioff, Aviad Rubinstein, Xizhi Tan et al.

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).

Moshe Babaioff, Amitai Frey, Noam Nisan

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.

Noga Alon, Moshe Babaioff, Yannai A. Gonczarowski et al.

In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter convergence bounds for extreme values of the CDF. We apply our bound in the context of revenue learning, which is a well-studied problem in economics and algorithmic game theory. We derive sample-complexity bounds on the uniform convergence rate of the empirical revenues to the true revenues, assuming a bound on the $k$th moment of the valuations, for any (possibly fractional) $k>1$. For uniform convergence in the limit, we give a complete characterization and a zero-one law: if the first moment of the valuations is finite, then uniform convergence almost surely occurs; conversely, if the first moment is infinite, then uniform convergence almost never occurs.