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(Im)possibility of Incentive Design for Challenge-based Blockchain Protocols

Suhyeon Lee, Dieu-Huyen Nguyen, Donghwan Lee

TL;DR

The paper studies incentive design for challenge-based off-chain computation in blockchains. It develops a mechanism-design model with a colluding minority, heterogeneous costs, and three ordering modes to evaluate ex-ante individual rationality for honest challengers $O_1$ and deterrence of fraudulent proposers $O_2$. The main results show that single-winner designs are either impossible or scale-limited to satisfy both goals, while multi-winner, non-exclusion designs admit a calibrated, scale-free parameter regime under reasonable costs and collusion. The work informs practical design choices for optimistic rollups, fraud proofs, and ZK-based dispute paths, with implications for deployment and performance.

Abstract

Blockchains offer a decentralized and secure execution environment strong enough to host cryptocurrencies, but the state-replication model makes on-chain computation expensive. To avoid heavy on-chain workloads, systems like Truebit and optimistic rollups use challenge-based protocols, performing computations off-chain and invoking the chain only when challenged. This keeps normal-case costs low and, if at least one honest challenger exists, can catch fraud. What has been less clear is whether honest challengers are actually incentivized and a dishonest proposer is properly damaged under the worst case environment. We build a model with a colluding minority, heterogeneous costs, and three ordering modes. We then ask whether two goals can be met together: honest non-loss and fraud deterrence. Our results are clear: in single-winner designs, the incentive design is impossible or limited in scale. By contrast, in multi-winner designs, we obtain simple, explicit conditions under which both goals hold.

(Im)possibility of Incentive Design for Challenge-based Blockchain Protocols

TL;DR

The paper studies incentive design for challenge-based off-chain computation in blockchains. It develops a mechanism-design model with a colluding minority, heterogeneous costs, and three ordering modes to evaluate ex-ante individual rationality for honest challengers and deterrence of fraudulent proposers . The main results show that single-winner designs are either impossible or scale-limited to satisfy both goals, while multi-winner, non-exclusion designs admit a calibrated, scale-free parameter regime under reasonable costs and collusion. The work informs practical design choices for optimistic rollups, fraud proofs, and ZK-based dispute paths, with implications for deployment and performance.

Abstract

Blockchains offer a decentralized and secure execution environment strong enough to host cryptocurrencies, but the state-replication model makes on-chain computation expensive. To avoid heavy on-chain workloads, systems like Truebit and optimistic rollups use challenge-based protocols, performing computations off-chain and invoking the chain only when challenged. This keeps normal-case costs low and, if at least one honest challenger exists, can catch fraud. What has been less clear is whether honest challengers are actually incentivized and a dishonest proposer is properly damaged under the worst case environment. We build a model with a colluding minority, heterogeneous costs, and three ordering modes. We then ask whether two goals can be met together: honest non-loss and fraud deterrence. Our results are clear: in single-winner designs, the incentive design is impossible or limited in scale. By contrast, in multi-winner designs, we obtain simple, explicit conditions under which both goals hold.
Paper Structure (24 sections, 8 theorems, 14 equations, 3 tables)

This paper contains 24 sections, 8 theorems, 14 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model and Design Goals
  4. Players, costs, and deposits
  5. Reward pool, winners, and splits
  6. Slashing.
  7. Winner set.
  8. Split rule.
  9. Ordering and fees: fair vs. unfair
  10. Key Parameters and Payoff Matrix
  11. Design goals
  12. Model Scope and Limitations
  13. Single-Winner: Impossibility and Scalability Limits
  14. U-P with single-winner: O1 fails
  15. U-B with single-winner: O1 is not guaranteed
  16. ...and 9 more sections

Key Result

lemma thmcounterlemma

To hold O1, it is necessary and sufficient that

Theorems & Definitions (16)

  • lemma thmcounterlemma: Worst-case lower bound on $\alpha$ for the reward goal O1
  • proof
  • lemma thmcounterlemma: Upper bound on $\alpha$ for the deterrence goal O2
  • proof
  • corollary thmcountercorollary: $\phi$-free nontrivial lower bound on $\eta$ for the deterrence goal O2
  • proof
  • theorem thmcountertheorem: O1 failure under U-P with a single winner
  • proof
  • theorem thmcountertheorem: O1 cannot be guaranteed under U-B with a single winner
  • proof
  • ...and 6 more