arXiv subjects

S. Matthew Weinberg

Publications and source records attributed to S. Matthew Weinberg.

At least 19 recordsLinked to original sources

arXiv2026

Single-Item Auctions with a Monopolist Intermediary

Classical optimal auction theory assumes that bids reach the seller directly. We study how this picture changes when a revenue-maximizing intermediary controls access to the seller's auction. Motivated by blockchain auctions, online platforms, and other intermediated markets, we consider a single-item auction with independent private values and a monopolist intermediary who can decide which bidder messages are forwarded to the seller. We establish approximation guarantees and impossibility results across three timing models: seller-first, intermediary-first, and simultaneous. In the seller-first model, arbitrary deterministic seller mechanisms collapse to posted-price mechanisms, and the intermediary's best response is a shifted Myerson auction. This yields a sharp separation: for regular distributions, the seller's revenue can be arbitrarily small relative to the no-intermediary optimum, while for $α$-strongly regular distributions, posted prices recover a constant fraction of the optimum with a tight dependence on $α$. We further show that timing matters: neither Stackelberg order uniformly dominates, and simultaneous play can leave both parties unboundedly worse off than in either sequential model.

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arXiv2026

Adversarial procurement in blockchains

An emerging blockchain protocol design pattern leverages the asymmetry between the computational effort in performing versus verifying tasks. For example, cryptographic validity proofs (e.g., SNARKS) require the prover to expend significant effort demonstrating the correctness of their claim, while the verifiers benefit from extremely easy validation. The operationalization of this paradigm requires efficiently soliciting the performance of expensive tasks in pseudonymous, adversarial environments. We formalize this as a mechanism design question. The protocol balances the economic cost of a liveness fault, where the work is not completed, with the payments required to incentivize specific behavior from candidate suppliers. We show that the loss of the optimal protocol scales logarithmically in the cost of a liveness fault, scaled up by the adversarial fraction of the network. Further, we find that the optimal equilibria have an intuitive structure, allowing us to provide concrete advice to practitioners. Specifically, in many regimes, the optimum designates a single, random node as the primary worker and a committee as a fallback, which is reminiscent of leader-based consensus mechanisms. We also characterize the asymptotic regimes where having negative payments (i.e., slashing in blockchain parlance) is especially helpful.

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arXiv2025

Analyzing the Economic Impact of Decentralization on Users

We model the ultimate price paid by users of a decentralized ledger as resulting from a two-stage game where Miners (/Proposers/etc.) first purchase blockspace via a Tullock contest, and then price that space to users. When analyzing our distributed ledger model, we find: - A characterization of all possible pure equilibria (although pure equilibria are not guaranteed to exist). - A natural sufficient condition, implied by Regularity (a la [Mye81]), for existence of a ''market-clearing'' pure equilibrium where Miners choose to sell all space allocated by the Distributed Ledger Protocol, and that this equilibrium is unique. - The market share of the largest miner is the relevant ''measure of decentralization'' to determine whether a market-clearing pure equilibrium exists. - Block rewards do not impact users' prices at equilibrium, when pure equilibria exist. But, higher block rewards can cause pure equilibria to exist. We also discuss aspects of our model and how they relate to blockchains deployed in practice. For example, only ''patient'' users (who are happy for their transactions to enter the blockchain under any miner) would enjoy the conclusions highlighted by our model, whereas ''impatient'' users (who are interested only for their transaction to be included in the very next block) still face monopoly pricing.

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arXiv2025

The Communication Complexity of Combinatorial Auctions with Additional Succinct Bidders

We study the communication complexity of welfare maximization in combinatorial auctions with bidders from either a standard valuation class (which require exponential communication to explicitly state, such as subadditive or XOS), or arbitrary succinct valuations (which can be fully described in polynomial communication, such as single-minded). Although succinct valuations can be efficiently communicated, we show that additional succinct bidders have a nontrivial impact on communication complexity of classical combinatorial auctions. Specifically, let $n$ be the number of subadditive/XOS bidders. We show that for SA $\cup$ SC (the union of subadditive and succinct valuations): (1) There is a polynomial communication $3$-approximation algorithm; (2) As $n \to \infty$, there is a matching $3$-hardness of approximation, which (a) is larger than the optimal approximation ratio of $2$ for SA, and (b) holds even for SA $\cup$ SM (the union of subadditive and single-minded valuations); and (3) For all $n \geq 3$, there is a constant separation between the optimal approximation ratios for SA $\cup$ SM and SA (and therefore between SA $\cup$ SC and SA as well). Similarly, we show that for XOS $\cup$ SC: (1) There is a polynomial communication $2$-approximation algorithm; (2) As $n \to \infty$, there is a matching $2$-hardness of approximation, which (a) is larger than the optimal approximation ratio of $e/(e-1)$ for XOS, and (b) holds even for XOS $\cup$ SM; and (3) For all $n \geq 2$, there is a constant separation between the optimal approximation ratios for XOS $\cup$ SM and XOS (and therefore between XOS $\cup$ SC and XOS as well).

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arXiv2025

Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms

Roughgarden (2020) initiates the study of Transaction Fee Mechanisms (TFMs), and posits that the on-chain game of a ``good'' TFM should be on-chain simple (OnCS), i.e., incentive compatible for users and the miner. Recent work of Ganesh, Thomas and Weinberg (2024) posits that they should additionally be Off-Chain Influence Proof (OffCIP), which means that the miner cannot achieve any additional revenue by separately conducting an off-chain auction to determine on-chain inclusion. They observe that a cryptographic second-price auction satisfies both properties, but leave open the question of whether other mechanisms (e.g, non-cryptographic) satisfy these properties. In this paper, we characterize OffCIP TFMs: They are those satisfying a burn identity relating the burn rule to the allocation rule. In particular, we show that auction is OffCIP if and only if its (induced direct-revelation) allocation rule $\bar{X}(\cdot)$ and burn rule $\bar{B}(\cdot)$ (both of which take as input users' values $v_1, \dots, v_n$) are truthful when viewing $\big(\bar{X}(\cdot), \bar{B}(\cdot)\big)$ as the allocation and pricing rule of a multi-item auction for a single additive buyer with values $\big(φ(v_1),\ldots, φ(v_n)\big)$ equal to the users' virtual values. Building on this burn identity, we characterize deterministic OffCIP and OnCS TFMs that do not use cryptography: They are posted-price mechanisms with specially-tuned burns. As a corollary, we show that such TFMs can only exist with infinite supply and prior-dependence. However, we show that for randomized TFMs, there are additional OnCS and OffCIP auctions that do not use cryptography (even when there is finite supply, under prior-dependence with a bounded prior distribution). Holistically, our results show that while OffCIP is a fairly stringent requirement, families of OffCIP mechanisms can be found for a variety of settings.

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arXiv2025

Optimal Single-Choice Prophet Inequalities from Samples

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant $\varepsilon > 0$, $O(n)$ samples from the distribution suffice to achieve the optimal competitive ratio ($\approx 0.745$) within $(1+\varepsilon)$, resolving an open problem of Correa, Dütting, Fischer, and Schewior.

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arXiv2025

Selfish Mining under General Stochastic Rewards

Selfish miners selectively withhold blocks to earn disproportionately high revenue. The vast majority of the selfish mining literature focuses exclusively on block rewards. Carlsten et al. [2016] is a notable exception, observing that similar strategic behavior is profitable in a zero-block-reward regime (the endgame for Bitcoin's quadrennial halving schedule) if miners are compensated with transaction fees alone. Neither model fully captures miner incentives today. The block reward remains 3.125 BTC, yet some blocks yield significantly higher revenue. For example, congestion during the launch of the Babylon protocol in August 2024 caused transaction fees to spike to 9.52 BTC. Our results are both practical and theoretical. Of practical interest, we study selfish mining profitability under a combined reward function that more accurately models miner incentives. This analysis enables us to make quantitative claims about protocol risk (e.g., the mining power at which a selfish strategy becomes profitable is reduced by 22% when optimizing over the combined reward function versus block rewards alone) and qualitative observations (e.g., a miner considering both block rewards and transaction fees will mine more or less aggressively respectively). These practical results follow from our novel model and methodology, which constitute our theoretical contributions. We model general, time-accruing stochastic rewards, which requires explicit treatment of difficult adjustment and randomness; we characterize reward function structure through a set of properties (e.g., that rewards accrue only as a function of time). We present a new methodology to analytically calculate expected selfish miner rewards under a broad class of stochastic reward functions and validate our method numerically by comparing it with the existing literature and simulating the combined reward sources directly.

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arXiv2025

Competition Complexity in Multi-Item Auctions: Beyond VCG and Regularity

We quantify the value of the monopoly's bargaining power in terms of competition complexity--that is, the number of additional bidders the monopoly must attract in simple auctions to match the expected revenue of the optimal mechanisms (c.f., Bulow and Klemperer, 1996, Eden et al., 2017)--within the setting of multi-item auctions. We show that for simple auctions that sell items separately, the competition complexity is $Θ(\frac{n}α)$ in an environment with $n$ original bidders under the slightly stronger assumption of $α$-strong regularity, in contrast to the standard regularity assumption in the literature, which requires $Ω(n \cdot \ln \frac{m}{n})$ additional bidders (Feldman et al., 2018). This significantly reduces the value of learning the distribution to design the optimal mechanisms, especially in large markets with many items for sale. For simple auctions that sell items as a grand bundle, we establish a constant competition complexity bound in a single-bidder environment when the number of items is small or when the value distribution has a monotone hazard rate. Some of our competition complexity results also hold when we compete against the first best benchmark (i.e., optimal social welfare).

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arXiv2024

A Bicriterion Concentration Inequality and Prophet Inequalities for $k$-Fold Matroid Unions

We investigate prophet inequalities with competitive ratios approaching $1$, seeking to generalize $k$-uniform matroids. We first show that large girth does not suffice: for all $k$, there exists a matroid of girth $\geq k$ and a prophet inequality instance on that matroid whose optimal competitive ratio is $\frac{1}{2}$. Next, we show $k$-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio $1-O(\sqrt{\frac{\log k}{k}})$ for any $k$-fold matroid union. Our prophet inequality follows from an online contention resolution scheme. The key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone $1$-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields "Chernoff-strength" concentration for a $1$-Lipschitz function that is not (approximately) self-bounding.

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arXiv2024

Revisiting the Primitives of Transaction Fee Mechanism Design

Transaction Fee Mechanism Design studies auctions run by untrusted miners for transaction inclusion in a blockchain. Under previously-considered desiderata, an auction is considered `good' if, informally-speaking, each party (i.e., the miner, the users, and coalitions of both miners and users) has no incentive to deviate from the fixed and pre-determined protocol. In this paper, we propose a novel desideratum for transaction fee mechanisms. We say that a TFM is off-chain influence proof when the miner cannot achieve additional revenue by running a separate auction off-chain. While the previously-highlighted EIP-1559 is the gold-standard according to prior desiderata, we show that it does not satisfy off-chain influence proofness. Intuitively, this holds because a Bayesian revenue-maximizing miner can strictly increase profits by persuasively threatening to censor any bids that do not transfer a tip directly to the miner off-chain. On the other hand, we reconsider the Cryptographic (multi-party computation assisted) Second Price Auction mechanism, which is technically not `simple for miners' according to previous desiderata (since miners may wish to set a reserve by fabricating bids). We show that, in a slightly different model where the miner is allowed to set the reserve directly, this auction satisfies simplicity for users and miners, and off-chain influence proofness. Finally, we prove a strong impossibility result: no mechanism satisfies all previously-considered properties along with off-chain influence proofness, even with unlimited supply, and even after soliciting input from the miner.

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arXiv2024

Optimal RANDAO Manipulation in Ethereum

It is well-known that RANDAO manipulation is possible in Ethereum if an adversary controls the proposers assigned to the last slots in an epoch. We provide a methodology to compute, for any fraction $α$ of stake owned by an adversary, the maximum fraction $f(α)$ of rounds that a strategic adversary can propose. We further implement our methodology and compute $f(\cdot)$ for all $α$. For example, we conclude that an optimal strategic participant with $5\%$ of the stake can propose a $5.048\%$ fraction of rounds, $10\%$ of the stake can propose a $10.19\%$ fraction of rounds, and $20\%$ of the stake can propose a $20.68\%$ fraction of rounds.

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arXiv2024

Communication Separations for Truthful Auctions: Breaking the Two-Player Barrier

We study the communication complexity of truthful combinatorial auctions, and in particular the case where valuations are either subadditive or single-minded, which we denote with $\mathsf{SubAdd}\cup\mathsf{SingleM}$. We show that for three bidders with valuations in $\mathsf{SubAdd}\cup\mathsf{SingleM}$, any deterministic truthful mechanism that achieves at least a $0.366$-approximation requires $\exp(m)$ communication. In contrast, a natural extension of [Fei09] yields a non-truthful $\mathrm{poly}(m)$-communication protocol that achieves a $\frac{1}{2}$-approximation, demonstrating a gap between the power of truthful mechanisms and non-truthful protocols for this problem. Our approach follows the taxation complexity framework laid out in [Dob16b], but applies this framework in a setting not encompassed by the techniques used in past work. In particular, the only successful prior application of this framework uses a reduction to simultaneous protocols which only applies for two bidders [AKSW20], whereas our three-player lower bounds are stronger than what can possibly arise from a two-player construction (since a trivial truthful auction guarantees a $\frac{1}{2}$-approximation for two players).

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arXiv2024

Profitable Manipulations of Cryptographic Self-Selection are Statistically Detectable

Cryptographic Self-Selection is a common primitive underlying leader-selection for Proof-of-Stake blockchain protocols. The concept was first popularized in Algorand [CM19], who also observed that the protocol might be manipulable. [FHWY22] provide a concrete manipulation that is strictly profitable for a staker of any size (and also prove upper bounds on the gains from manipulation). Separately, [YSZ23, BM24] initiate the study of undetectable profitable manipulations of consensus protocols with a focus on the seminal Selfish Mining strategy [ES14] for Bitcoin's Proof-of-Work longest-chain protocol. They design a Selfish Mining variant that, for sufficiently large miners, is strictly profitable yet also indistinguishable to an onlooker from routine latency (that is, a sufficiently large profit-maximizing miner could use their strategy to strictly profit over being honest in a way that still appears to the rest of the network as though everyone is honest but experiencing mildly higher latency. This avoids any risk of negatively impacting the value of the underlying cryptocurrency due to attack detection). We investigate the detectability of profitable manipulations of the canonical cryptographic self-selection leader selection protocol introduced in [CM19] and studied in [FHWY22], and establish that for any player with $α< \frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the total stake, every strictly profitable manipulation is statistically detectable. Specifically, we consider an onlooker who sees only the random seed of each round (and does not need to see any other broadcasts by any other players). We show that the distribution of the sequence of random seeds when any player is profitably manipulating the protocol is inconsistent with any distribution that could arise by honest stakers being offline or timing out (for a natural stylized model of honest timeouts).

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arXiv2024

Computing Optimal Manipulations in Cryptographic Self-Selection Proof-of-Stake Protocols

Cryptographic Self-Selection is a paradigm employed by modern Proof-of-Stake consensus protocols to select a block-proposing "leader." Algorand [Chen and Micali, 2019] proposes a canonical protocol, and Ferreira et al. [2022] establish bounds $f(α,β)$ on the maximum fraction of rounds a strategic player can lead as a function of their stake $α$ and a network connectivity parameter $β$. While both their lower and upper bounds are non-trivial, there is a substantial gap between them (for example, they establish $f(10\%,1) \in [10.08\%, 21.12\%]$), leaving open the question of how significant of a concern these manipulations are. We develop computational methods to provably nail $f(α,β)$ for any desired $(α,β)$ up to arbitrary precision, and implement our method on a wide range of parameters (for example, we confirm $f(10\%,1) \in [10.08\%, 10.15\%]$). Methodologically, estimating $f(α,β)$ can be phrased as estimating to high precision the value of a Markov Decision Process whose states are countably-long lists of real numbers. Our methodological contributions involve (a) reformulating the question instead as computing to high precision the expected value of a distribution that is a fixed-point of a non-linear sampling operator, and (b) provably bounding the error induced by various truncations and sampling estimations of this distribution (which appears intractable to solve in closed form). One technical challenge, for example, is that natural sampling-based estimates of the mean of our target distribution are \emph{not} unbiased estimators, and therefore our methods necessarily go beyond claiming sufficiently-many samples to be close to the mean.

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arXiv2024

On the cut-query complexity of approximating max-cut

We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [RSW18]. Graph algorithms in this cut query model and other query models have recently been studied for various other problems such as min-cut, connectivity, bipartiteness, and triangle detection. Max-cut in the cut query model can also be viewed as a natural special case of submodular function maximization: on query $S \subseteq V$, the oracle returns the total weight of the cut between $S$ and $V \backslash S$. Our first main technical result is a lower bound stating that a deterministic algorithm achieving a $c$-approximation for any $c > 1/2$ requires $Ω(n)$ queries. This uses an extension of the cut dimension to rule out approximation (prior work of [GPRW20] introducing the cut dimension only rules out exact solutions). Secondly, we provide a randomized algorithm with $\tilde{O}(n)$ queries that finds a $c$-approximation for any $c < 1$. We achieve this using a query-efficient sparsifier for undirected weighted graphs (prior work of [RSW18] holds only for unweighted graphs). To complement these results, for most constants $c \in (0,1]$, we nail down the query complexity of achieving a $c$-approximation, for both deterministic and randomized algorithms (up to logarithmic factors). Analogously to general submodular function maximization in the same model, we observe a phase transition at $c = 1/2$: we design a deterministic algorithm for global $c$-approximate max-cut in $O(\log n)$ queries for any $c < 1/2$, and show that any randomized algorithm requires $Ω(n/\log n)$ queries to find a $c$-approximate max-cut for any $c > 1/2$. Additionally, we show that any deterministic algorithm requires $Ω(n^2)$ queries to find an exact max-cut (enough to learn the entire graph).

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arXiv2024

Settling the Communication Complexity of VCG-based Mechanisms for all Approximation Guarantees

We consider truthful combinatorial auctions with items $M = [m]$ for sale to $n$ bidders, where each bidder $i$ has a private monotone valuation $v_i : 2^M \to R_+$. Among truthful mechanisms, maximal-in-range (MIR) mechanisms achieve the best-known approximation guarantees among all poly-communication deterministic truthful mechanisms in all previously-studied settings. Our work settles the communication necessary to achieve any approximation guarantee via an MIR mechanism. Specifically: Let MIRsubmod$(m,k)$ denote the best approximation guarantee achievable by an MIR mechanism using $2^k$ communication between bidders with submodular valuations over $m$ items. Then for all $k = Ω(\log(m))$, MIRsubmod$(m,k) = Ω(\sqrt{m/(k\log(m/k))})$. When $k = Θ(\log(m))$, this improves the previous best lower bound for poly-comm. MIR mechanisms from $Ω(m^{1/3}/\log^{2/3}(m))$ to $Ω(\sqrt{m}/\log(m))$. We also have MIRsubmod$(m,k) = O(\sqrt{m/k})$. Moreover, our mechanism is optimal w.r.t. the value query and succinct representation models. When $k = Θ(\log(m))$, this improves the previous best approximation guarantee for poly-comm. MIR mechanisms from $O(\sqrt{m})$ to $O(\sqrt{m/\log(m)})$. Let also MIRgen$(m,k)$ denote the best approximation guarantee achievable by an MIR mechanism using $2^k$ communication between bidders with general valuations over $m$ items. Then for all $k = Ω(\log(m))$, MIRgen$(m,k) = Ω(m/k)$. When $k = Θ(\log(m))$, this improves the previous best lower bound for poly-comm. MIR mechanisms from $Ω(m/\log^2(m))$ to $Ω(m/\log(m))$. We also have MIRgen$(m,k) = O(m/k)$. Moreover, our mechanism is optimal w.r.t. the value query and succinct representation models. When $k = Θ(\log(m))$, this improves the previous best approximation guarantee for poly-comm. MIR mechanisms from $O(m/\sqrt{\log(m)})$ to $O(m/\log(m))$.

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arXiv2024

Settling the Competition Complexity of Additive Buyers over Independent Items

The competition complexity of an auction setting is the number of additional bidders needed such that the simple mechanism of selling items separately (with additional bidders) achieves greater revenue than the optimal but complex (randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the additional bidders. Our main result settles the competition complexity of $n$ bidders with additive values over $m < n$ independent items at $Θ(\sqrt{nm})$. The $O(\sqrt{nm})$ upper bound is due to [BW19], and our main result improves the prior lower bound of $Ω(\ln n)$ to $Ω(\sqrt{nm})$. Our main result follows from an explicit construction of a Bayesian IC auction for $n$ bidders with additive values over $m m$: $\text{SRev}_n(\mathcal{ER}^m) = nm+O_m(\ln (n)) \leq \text{SRev}_{n+O_m(\ln (n))}(\mathcal{ER}^m)$, and therefore our result can only follow by considering all possible truncations.

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arXiv2024

Undetectable Selfish Mining

Seminal work of Eyal and Sirer (2014) establishes that a strategic Bitcoin miner may strictly profit by deviating from the intended Bitcoin protocol, using a strategy now termed *selfish mining*. More specifically, any miner with $>1/3$ of the total hashrate can earn bitcoin at a faster rate by selfish mining than by following the intended protocol (depending on network conditions, a lower fraction of hashrate may also suffice). One convincing critique of selfish mining in practice is that the presence of a selfish miner is *statistically detectable*: the pattern of orphaned blocks created by the presence of a selfish miner cannot be explained by natural network delays. Therefore, if an attacker chooses to selfish mine, users can detect this, and this may (significantly) negatively impact the value of BTC. So while the attacker may get slightly more bitcoin by selfish mining, these bitcoin may be worth significantly less USD. We develop a selfish mining variant that is provably *statistically undetectable*: the pattern of orphaned blocks is statistically identical to a world with only honest miners but higher network delay. Specifically, we consider a stylized model where honest miners with network delay produce orphaned blocks at each height independently with probability $β'$. We propose a selfish mining strategy that instead produces orphaned blocks at each height independently with probability $β> β'$. We further show that our strategy is strictly profitable for attackers with $38.2\% \ll 50\%$ of the total hashrate (and this holds for all natural orphan rates $β'$).

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