arXiv subjects

Ben Berger

Publications and source records attributed to Ben Berger.

7 recordsLinked to original sources

arXiv2025

Economic Censorship Games in Fraud Proofs

Optimistic rollups rely on fraud proofs -- interactive protocols executed on Ethereum to resolve conflicting claims about the rollup's state -- to scale Ethereum securely. To mitigate against potential censorship of protocol moves, fraud proofs grant participants a significant time window, known as the challenge period, to ensure their moves are processed on chain. Major optimistic rollups today set this period at roughly one week, mainly to guard against strong censorship that undermines Ethereum's own crypto-economic security. However, other forms of censorship are possible, and their implication on optimistic rollup security is not well understood. This paper considers economic censorship attacks, where an attacker censors the defender's transactions by bribing block proposers. At each step, the attacker can either censor the defender -- depleting the defender's time allowance at the cost of the bribe -- or allow the current transaction through while conserving funds for future censorship. We analyze three game theoretic models of these dynamics and determine the challenge period length required to ensure the defender's success, as a function of the number of required protocol moves and the players' available budgets.

cs.GT↗

arXiv2024

Pandora's Box Problem With Time Constraints

The Pandora's Box problem models the search for the best alternative when evaluation is costly. In the simplest variant, a decision maker is presented with $n$ boxes, each associated with a cost of inspection and a hidden random reward. The decision maker inspects a subset of these boxes one after the other, in a possibly adaptive order, and gains the difference between the largest revealed reward and the sum of the inspection costs. Although this classic version is well understood (Weitzman 1979), there is a flourishing recent literature on variants of the problem. Here we introduce a general framework -- the Pandora's Box Over Time problem -- that captures a wide range of variants where time plays a role, e.g., by constraining the schedules of exploration and influencing costs and rewards. In our framework, boxes have time-dependent rewards and costs, whereas inspection may require a box-specific processing time. Moreover, once a box is inspected, its reward may deteriorate over time. Our main result is an efficient constant-factor approximation to the optimal strategy for the Pandora's Box Over Time problem, which is generally NP-hard to compute. We further obtain improved results for the natural special cases where boxes have no processing time, boxes are available only in specific time slots, or when costs and reward distributions are time-independent (but rewards may still deteriorate after inspection).

cs.GT↗

arXiv2024

BoLD: Fast and Cheap Dispute Resolution

BoLD is a new dispute resolution protocol that is designed to replace the originally deployed Arbitrum dispute resolution protocol. Unlike that protocol, BoLD is resistant to delay attacks. It achieves this resistance without a significant increase in onchain computation costs and with reduced staking costs.

cs.CR↗

arXiv2023

Learning-Augmented Metric Distortion via $(p,q)$-Veto Core

In the metric distortion problem there is a set of candidates $C$ and voters $V$ in the same metric space. The goal is to select a candidate minimizing the social cost: the sum of distances of the selected candidate from all the voters, and the challenge arises from the algorithm receiving only ordinaL input: each voter's ranking of candidate, while the objective function is cardinal, determined by the underlying metric. The distortion of an algorithm is its worst-case approximation factor of the optimal social cost. A key concept here is the (p,q)-veto core, with $p\in \Delta(V)$ and $q\in \Delta(C)$ being normalized weight vectors representing voters' veto power and candidates' support, respectively. The (p,q)-veto core corresponds to a set of winners from a specific class of deterministic algorithms. Notably, the optimal distortion of $3$ is obtained from this class, by selecting veto core candidates using uniform $p$ and $q$ proportional to candidates' plurality scores. Bounding the distortion of other algorithms from this class is an open problem. Our contribution is twofold. First, we establish upper bounds on the distortion of candidates from the (p,q)-veto core for arbitrary weight vectors $p$ and $q$. Second, we revisit the metric distortion problem through the \emph{learning-augmented} framework, which equips the algorithm with a (machine-learned) prediction regarding the optimal candidate. The quality of this prediction is unknown, and the goal is to optimize the algorithm's performance under accurate predictions (consistency), while simultaneously providing worst-case guarantees under arbitrarily inaccurate predictions (robustness). We propose an algorithm that chooses candidates from the (p,q)-veto core, using a prediction-guided q vector and, leveraging our distortion bounds, we prove that this algorithm achieves the optimal robustness-consistency trade-off.

cs.GT↗

arXiv2023

Pandora's Problem with Combinatorial Cost

Pandora's problem is a fundamental model in economics that studies optimal search strategies under costly inspection. In this paper we initiate the study of Pandora's problem with combinatorial costs, capturing many real-life scenarios where search cost is non-additive. Weitzman's celebrated algorithm [1979] establishes the remarkable result that, for additive costs, the optimal search strategy is non-adaptive and computationally feasible. We inquire to which extent this structural and computational simplicity extends beyond additive cost functions. Our main result is that the class of submodular cost functions admits an optimal strategy that follows a fixed, non-adaptive order, thus preserving the structural simplicity of additive cost functions. In contrast, for the more general class of subadditive (or even XOS) cost functions, the optimal strategy may already need to determine the search order adaptively. On the computational side, obtaining any approximation to the optimal utility requires super polynomially many queries to the cost function, even for a strict subclass of submodular cost functions.

cs.DS↗

arXiv2021

(Almost Full) EFX Exists for Four Agents (and Beyond)

The existence of EFX allocations is a major open problem in fair division, even for additive valuations. The current state of the art is that no setting where EFX allocations are impossible is known, and EFX is known to exist for ($i$) agents with identical valuations, ($ii$) 2 agents, ($iii$) 3 agents with additive valuations, ($iv$) agents with one of two additive valuations and ($v$) agents with two-valued instances. It is also known that EFX exists if one can leave $n-1$ items unallocated, where $n$ is the number of agents. We develop new techniques that allow us to push the boundaries of the enigmatic EFX problem beyond these known results, and, arguably, to simplify proofs of earlier results. Our main results are ($i$) every setting with 4 additive agents admits an EFX allocation that leaves at most a single item unallocated, ($ii$) every setting with $n$ additive valuations has an EFX allocation with at most $n-2$ unallocated items. Moreover, all of our results extend beyond additive valuations to all nice cancelable valuations (a new class, including additive, unit-demand, budget-additive and multiplicative valuations, among others). Furthermore, using our new techniques, we show that previous results for additive valuations extend to nice cancelable valuations.

cs.GT↗

arXiv2020

On the Power and Limits of Dynamic Pricing in Combinatorial Markets

We study the power and limits of optimal dynamic pricing in combinatorial markets; i.e., dynamic pricing that leads to optimal social welfare. Previous work by Cohen-Addad et al. [EC'16] demonstrated the existence of optimal dynamic prices for unit-demand buyers, and showed a market with coverage valuations that admits no such prices. However, finding the frontier of markets (i.e., valuation functions) that admit optimal dynamic prices remains an open problem. In this work we establish positive and negative results that narrow the existing gap. On the positive side, we provide tools for handling markets beyond unit-demand valuations. In particular, we characterize all optimal allocations in multi-demand markets. This characterization allows us to partition the items into equivalence classes according to the role they play in achieving optimality. Using these tools, we provide a poly-time optimal dynamic pricing algorithm for up to $3$ multi-demand buyers. On the negative side, we establish a maximal domain theorem, showing that for every non-gross substitutes valuation, there exist unit-demand valuations such that adding them yields a market that does not admit an optimal dynamic pricing. This result is the dynamic pricing equivalent of the seminal maximal domain theorem by Gul and Stacchetti [JET'99] for Walrasian equilibrium. Yang [JET'17] discovered an error in their original proof, and established a different, incomparable version of their maximal domain theorem. En route to our maximal domain theorem for optimal dynamic pricing, we provide the first complete proof of the original theorem by Gul and Stacchetti.

cs.GT↗