A Game-Theoretic Approach to the Study of Blockchain's Robustness

TL;DR

This work analyzes the robustness of blockchains, focusing on Ethereum PoS, by combining distributed-computing formalism with game-theoretic modeling. It formalizes the Ethereum PoS protocol, studies safety and liveness, and introduces the inactivity leak as an incentive mechanism with potential safety risks. It then uses game theory to explore rational validator behavior, showing that while the system tends toward obedience under typical conditions, incentive design can create exploitable vulnerabilities (e.g., probabilistic liveness attacks). The findings highlight the delicate balance between availability, finality, and incentives, offering design insights for more resilient PoS protocols and guiding future research on incentive-compatible, secure blockchain systems.

Abstract

Blockchains have sparked global interest in recent years, gaining importance as they increasingly influence technology and finance. This thesis investigates the robustness of blockchain protocols, specifically focusing on Ethereum Proof-of-Stake. We define robustness in terms of two critical properties: Safety, which ensures that the blockchain will not have permanent conflicting blocks, and Liveness, which guarantees the continuous addition of new reliable blocks. Our research addresses the gap between traditional distributed systems approaches, which classify agents as either honest or Byzantine (i.e., malicious or faulty), and game-theoretic models that consider rational agents driven by incentives. We explore how incentives impact the robustness with both approaches. The thesis comprises three distinct analyses. First, we formalize the Ethereum PoS protocol, defining its properties and examining potential vulnerabilities through a distributed systems perspective. We identify that certain attacks can undermine the system's robustness. Second, we analyze the inactivity leak mechanism, a critical feature of Ethereum PoS, highlighting its role in maintaining system liveness during network disruptions but at the cost of safety. Finally, we employ game-theoretic models to study the strategies of rational validators within Ethereum PoS, identifying conditions under which these agents might deviate from the prescribed protocol to maximize their rewards. Our findings contribute to a deeper understanding of the importance of incentive mechanisms for blockchain robustness and provide insights into designing more resilient blockchain protocols.

Figures (27)

• Figure 1: Simplified representation of a Bitcoin block.
• Figure 2: Ethereum protocol Structure
• Figure 3: The figure depicts the finalization scenario of Case 1 with the 3 steps from top to bottom. We represent a checkpoint with a hexagon, a justified checkpoint with a double hexagon, and a finalized checkpoint with a colored double hexagon. The arrow between two checkpoints indicates a supermajority link.
• Figure 4: The figure depicts the finalization scenario of Case 2 with the 3 steps from top to bottom. We represent a checkpoint with a hexagon, a justified checkpoint with a double hexagon, and a finalized checkpoint with double hexagon coloured. The arrow between two checkpoints indicates a supermajority link.
• Figure 5: This figure illustrates the case of two checkpoints $A$ and $C$ respecting all the conditions for finalization but the one that stipulates that a checkpoint $B$ in-between must be justified for $A$ to be finalized.

Theorems & Definitions (39)

• Definition III.1: Consensus
• Definition V.1: Canonical chain
• Definition V.2: Finalized block
• Definition V.3: Finalized chain
• Lemma V.1
• proof
• Lemma V.2
• proof
• Theorem V.1: Safety
• proof