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Economic Censorship Games in Fraud Proofs

Ben Berger, Edward W. Felten, Akaki Mamageishvili, Benny Sudakov

TL;DR

The paper tackles economic censorship in fraud proofs for optimistic rollups by modeling defender-attacker interactions as multi-round games with budgets and challenge periods. It develops three core models—G^1, G^1_k, and G^m—to derive budget-threshold conditions under which either defender or attacker can guarantee victory, including linear-in-budget thresholds and recurrences that govern optimal play. It extends the analysis to probabilistic round types and multi-proposer settings, proving near-optimal simple strategies in many regimes and providing dynamic-programming tools to compute thresholds. The evaluation with Arbitrum BoLD parameters demonstrates practical security implications: defender budgets scale with number of rounds and builders, while higher proposer counts reduce required defender funding, informing design choices for robust fraud-proof mechanisms. Overall, the work clarifies how economic incentives shape censorship resilience in fraud proofs and offers concrete guidance for setting challenge periods and defense budgets.

Abstract

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.

Economic Censorship Games in Fraud Proofs

TL;DR

The paper tackles economic censorship in fraud proofs for optimistic rollups by modeling defender-attacker interactions as multi-round games with budgets and challenge periods. It develops three core models—G^1, G^1_k, and G^m—to derive budget-threshold conditions under which either defender or attacker can guarantee victory, including linear-in-budget thresholds and recurrences that govern optimal play. It extends the analysis to probabilistic round types and multi-proposer settings, proving near-optimal simple strategies in many regimes and providing dynamic-programming tools to compute thresholds. The evaluation with Arbitrum BoLD parameters demonstrates practical security implications: defender budgets scale with number of rounds and builders, while higher proposer counts reduce required defender funding, informing design choices for robust fraud-proof mechanisms. Overall, the work clarifies how economic incentives shape censorship resilience in fraud proofs and offers concrete guidance for setting challenge periods and defense budgets.

Abstract

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.

Paper Structure

This paper contains 17 sections, 10 theorems, 31 equations.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. $\mathcal{G}^1$ Game.
  4. $\mathcal{G}^1_k$ Game.
  5. $\mathcal{G}^m$ Game.
  6. Related Literature
  7. Preliminaries
  8. $\mathcal{G}^1$ Game
  9. $\mathcal{G}^1_k$ Game
  10. Analysis
  11. A Probabilistic Variant of $\mathcal{G}^1_k$
  12. $\mathcal{G}^m$ Game
  13. Analysis of the Budget-Balanced Mechanism
  14. Analyis of the Conditional Payment Mechanism
  15. Evaluation
  16. ...and 2 more sections

Key Result

Theorem 1

Alice has a winning strategy in $\mathcal{G}^1$ with parameters $T,N,D,A$ iff

Theorems & Definitions (21)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Remark 1
  • Theorem 3
  • proof
  • Corollary 1
  • ...and 11 more