arXiv subjects

Ariel Shaulker

Publications and source records attributed to Ariel Shaulker.

6 recordsLinked to original sources

arXiv2026

Welfare Maximization in Bilateral Trade: Improved Approximation Guarantees Beyond the Fixed Price Barrier

We study the setting of welfare maximization in bilateral trade, where the values of both the buyer and the seller are drawn from independent distributions. Our goal is to maximize social welfare. In this setting, fixed price mechanisms have been extensively studied. In a fixed price mechanism, there is a price $p$ that depends only on the distributions of the buyer and the seller. Trade occurs if and only if the buyer's value is at least $p$ and the seller's value is at most $p$. A long line of work has culminated in determining almost exactly the approximation ratios achievable by fixed price mechanisms: there exists a fixed price mechanism that obtains at least a $0.72$ fraction of the social welfare, but no fixed price mechanism can guarantee more than a $0.7381$ fraction of it [Cai and Wu, STOC'23; Liu, Ren, and Wang, STOC'23]. No other incentive-compatible mechanism is known to beat the performance of fixed-price mechanisms in this setting. This paper shows how to achieve a larger fraction of the optimal welfare with other classes of mechanisms. Specifically, we study the buyer-offering mechanism with a reserve price. In this mechanism, the buyer observes its value and makes a take-it-or-leave-it offer to the seller, where the offer is at least the reserve price. Beyond its simplicity, this natural mechanism is attractive because the seller always has a dominant strategy: accept the offer if its value is at most the offer, and otherwise reject it. We show that there always exists a reserve price that guarantees a $0.746$ fraction of the social welfare. This not only improves upon the best previously known approximation guarantee for the problem, but also demonstrates that fixed-price mechanisms are not optimal in this setting.

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arXiv2025

Interdependent Bilateral Trade: Information vs Approximation

Welfare maximization in bilateral trade has been extensively studied in recent years. Previous literature obtained incentive-compatible approximation mechanisms only for the private values case. In this paper, we study welfare maximization in bilateral trade with interdependent values. Designing mechanisms for interdependent settings is much more challenging because the values of the players depend on the private information of the others, requiring complex belief updates and strategic inference. We propose to classify information structures by quantifying the influence that a player's private signal has on their own valuation. We then paint a picture of where approximations are possible and impossible based on these information structures. Finally, we also study the possible approximation ratios for a natural family of information structures.

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arXiv2025

Multi-Parameter Mechanisms for Consumer Surplus Maximization

We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller with a set of goods faces a set of strategic buyers with private values, each of whom aims to maximize their own individual utility. The seller, in contrast, aims to allocate the goods in a way which maximizes the total buyer utility. The seller must then elicit the values of the buyers in order to decide what goods to award each buyer. The canonical approach in mechanism design to ensure truthful reporting of the private information is to find appropriate prices to charge each buyer in order to align their objective with the objective of the seller. Indeed, there are many celebrated results to this end when the seller's objective is welfare maximization [Clarke, 1971, Groves, 1973, Vickrey, 1961] or revenue maximization [Myerson, 1981]. However, in the case of consumer surplus maximization the picture is less clear -- using high payments to ensure the highest value bidders are served necessarily decreases their surplus utility, but using low payments may lead the seller into serving lower value bidders. Our main result in this paper is a framework for designing mechanisms which maximize consumer surplus. We instantiate our framework in a variety of canonical multi-parameter auction settings (i.e., unit-demand bidders with heterogeneous items, multi-unit auctions, and auctions with divisible goods) and use it to design auctions achieving consumer surplus with optimal approximation guarantees against the total social welfare. Along the way, we answer an open question posed by Hartline and Roughgarden [2008] for the two bidders single item setting.

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arXiv2024

Bilateral Trade with Correlated Values

We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the case where the values of the buyer and the seller are drawn from independent distributions. In this paper, we study bilateral trade mechanisms when the values are drawn from a joint distribution. We prove that the buyer-offering mechanism guarantees an approximation ratio of $\frac e {e-1} \approx 1.582$ to the social welfare even if the values are drawn from a joint distribution. The buyer-offering mechanism is Bayesian incentive compatible, but the seller has a dominant strategy. We prove the buyer-offering mechanism is optimal in the sense that no Bayesian mechanism where one of the players has a dominant strategy can obtain an approximation ratio better than $\frac e {e-1}$. We also show that no mechanism in which both sides have a dominant strategy can provide any constant approximation to the social welfare when the values are drawn from a joint distribution. Finally, we prove some impossibility results on the power of general Bayesian incentive compatible mechanisms. In particular, we show that no deterministic Bayesian incentive-compatible mechanism can provide an approximation ratio better than $1+\frac {\ln 2} 2\approx 1.346$.

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arXiv2022

Rigidity in Mechanism Design and its Applications

We introduce the notion of rigidity in auction design and use it to analyze some fundamental aspects of mechanism design. We focus on single-item auctions where the values of the bidders are drawn from some (possibly correlated) distribution $\mathcal F$. Let $f$ be the allocation function of an optimal mechanism for $\mathcal F$. Informally, $S$ is (linearly) rigid in $\mathcal F$ if for every mechanism $M'$ with an allocation function $f'$ where $f$ and $f'$ agree on the allocation of at most $x$-fraction of the instances of $S$, the expected revenue of $M'$ is at most an $x$ fraction of the optimal revenue. We use rigidity to explain the singular success of Cremer and McLean's auction. Recall that the revenue of Cremer and McLean's auction is the optimal welfare if the distribution obeys a certain ``full rank'' condition, but no analogous constructions are known if this condition does not hold. Note that the Kolmogorov complexity of the allocation function of Cremer and McLean's auction is logarithmic, whereas we use rigidity to show that for some distributions that do not obey the full rank condition, the Kolmogorov complexity of the allocation function of every mechanism that provides a constant approximation is almost linear. We further investigate rigidity assuming different notions of individual rationality. Assuming ex-post individual rationality, if there is a rigid set, the structure of the optimal mechanism is simple: the player with the highest value ``usually'' wins the item and contributes most of the revenue. In contrast, assuming interim individual rationality, there are distributions with a rigid set $S$ where the optimal mechanism has no obvious allocation pattern (i.e., its Kolmogorov complexity is high). Our results help explain why we have little hope of developing good, simple and generic approximation mechanisms in the interim individual rationality world.

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arXiv2020

Improved Lower Bounds for Truthful Scheduling

The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of $\min(m,n)$, where $n$ is the number of machines and $m$ is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than $2$. Since then, the lower bound was improved to $1 +\sqrt 2 \approx 2.41$ by Christodoulou, Kotsoupias, and Vidali, and then to $1+ϕ\approx 2.618$ by Kotsoupias and Vidali. Very recently, the lower bound was improved to $2.755$ by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to $3-δ$, for every constant $δ>0$. Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known $1+\sqrt{2}$ lower bound requires at least $3$ machines and $5$ jobs. In contrast, we show a lower bound of $2.2055$ that uses only $3$ machines and $3$ jobs and a lower bound of $1+\sqrt 2$ that uses only $3$ machines and $4$ jobs. For the case of two machines and two jobs we show a lower bound of $2$. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.

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