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Games in Public Announcement: How to Reduce System Losses in Optimistic Blockchain Mechanisms

Siyuan Liu, Yulong Zeng

TL;DR

The paper develops a game-theoretic model of announcement games in optimistic Layer-2 rollups, framing interaction between an Aggregator and Validators with deposits, rewards, and penalties. It derives a complete set of Nash equilibria across one, two, and N validators, including symmetric and asymmetric cases, and provides explicit loss expressions such as $\mathcal{L}=\beta(1-\alpha)Z$, illustrating how losses grow with the final block value $Z$ and change with system parameters. Through both analytical results and parameter analysis, it shows how compactly tuning deposits, rewards, and costs (and introducing a tie-breaking term $D$) can move the system toward lower-loss equilibria, including non-KYC variants. The work yields practical mechanism-design guidelines for reducing system losses in optimistic rollups and similar information-disclosure games, with insights into the trade-offs between security incentives, validator participation, and throughput. Overall, the results illuminate incentive-compatibility considerations for scalable, secure L2 architectures and offer concrete levers for protocol designers.

Abstract

Announcement games, where information is disseminated by announcers and challenged by validators, are prevalent in real-world scenarios. Validators take effort to verify the validity of the announcements, gaining rewards for successfully challenging invalid ones, while receiving nothing for valid ones. Optimistic Rollup, a Layer 2 blockchain scaling solution, exemplifies such games, offering significant improvements in transaction throughput and cost efficiency. We present a game-theoretic model of announcement games to analyze the potential behaviors of announcers and validators. We identify all Nash equilibria and study the corresponding system losses for different Nash equilibria. Additionally, we analyze the impact of various system parameters on system loss under the Nash equilibrium. Finally, we provide suggestions for mechanism optimization to reduce system losses.

Games in Public Announcement: How to Reduce System Losses in Optimistic Blockchain Mechanisms

TL;DR

The paper develops a game-theoretic model of announcement games in optimistic Layer-2 rollups, framing interaction between an Aggregator and Validators with deposits, rewards, and penalties. It derives a complete set of Nash equilibria across one, two, and N validators, including symmetric and asymmetric cases, and provides explicit loss expressions such as , illustrating how losses grow with the final block value and change with system parameters. Through both analytical results and parameter analysis, it shows how compactly tuning deposits, rewards, and costs (and introducing a tie-breaking term ) can move the system toward lower-loss equilibria, including non-KYC variants. The work yields practical mechanism-design guidelines for reducing system losses in optimistic rollups and similar information-disclosure games, with insights into the trade-offs between security incentives, validator participation, and throughput. Overall, the results illuminate incentive-compatibility considerations for scalable, secure L2 architectures and offer concrete levers for protocol designers.

Abstract

Announcement games, where information is disseminated by announcers and challenged by validators, are prevalent in real-world scenarios. Validators take effort to verify the validity of the announcements, gaining rewards for successfully challenging invalid ones, while receiving nothing for valid ones. Optimistic Rollup, a Layer 2 blockchain scaling solution, exemplifies such games, offering significant improvements in transaction throughput and cost efficiency. We present a game-theoretic model of announcement games to analyze the potential behaviors of announcers and validators. We identify all Nash equilibria and study the corresponding system losses for different Nash equilibria. Additionally, we analyze the impact of various system parameters on system loss under the Nash equilibrium. Finally, we provide suggestions for mechanism optimization to reduce system losses.
Paper Structure (32 sections, 16 theorems, 75 equations, 7 figures, 7 tables)

This paper contains 32 sections, 16 theorems, 75 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Model
  4. Parameters
  5. Payoff Matrix
  6. Multiple Players
  7. Equilibrium Analysis
  8. One validator
  9. Extension to two validators
  10. Extension to $n$ validators
  11. The Symmetric Case
  12. The Asymmetric Case
  13. Non-KYC Scenario
  14. Breaking Tie
  15. Suggestion
  16. ...and 17 more sections

Key Result

lemma thmcounterlemma

There is no pure strategy equilibrium between $\mathcal{A}$ and $\mathcal{V}$.

Figures (7)

  • Figure 1: The relationship between the probabilities $\alpha_1$ and $\alpha_2$ as the number of verifier $k$ changes.
  • Figure 2: The image of the $\beta$ as validators k and R changes. The solid line represents the general $\beta$ that exists for all k, while the dashed line represents the additional $\beta$ that appears as k changes.
  • Figure 3: The image of the $\beta$ as validators k and R changes. The solid line represents the general $\beta$ that exists for all k, while the dashed line represents the additional $\beta$ that appears as k changes.
  • Figure 4: The system loss $\mathcal{L}$ changes by $S$
  • Figure 5: The system loss $\mathcal{L}$ changes by $B$
  • ...and 2 more figures

Theorems & Definitions (30)

  • lemma thmcounterlemma
  • theorem thmcountertheorem
  • proof : Sketch
  • theorem thmcountertheorem
  • proof : Sketch
  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • lemma thmcounterlemma
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • ...and 20 more