[Paper Review] Staking Pools on Blockchains

Hans Gersbach, Akaki Mamageishvili+1 more|arXiv (Cornell University)|Mar 11, 2022

Blockchain Technology Applications and Security4 citations

TL;DR

This paper models staking pool formation in proof-of-stake blockchains using a game-theoretic framework, analyzing how reward distribution rules affect blockchain security and fairness. It establishes the existence and uniqueness of equilibria and shows that return competition can prevent malicious actors from dominating pools, while return fixing leads to systemic failure due to free-riding by honest agents.

ABSTRACT

On several proof-of-stake blockchains, agents engaged in validating transactions can open a pool to which others can delegate their stake in order to earn higher returns. We develop a model of staking pool formation in the presence of malicious agents and establish existence and uniqueness of equilibria. We then identify potential and risk of staking pools. First, allowing for staking pools lowers blockchain security. Yet, honest stake holders obtain higher returns. Second, by choosing welfare optimal distribution rewards, staking pools prevent that malicious agents receive large rewards. Third, when pool owners can freely distribute the returns from validation to delegators, staking pools disrupt blockchain operations, since malicious agents attract most delegators by offering generous returns.

Motivation & Objective

• To model staking pool formation in proof-of-stake blockchains under the presence of malicious agents.
• To analyze how different reward distribution mechanisms—return fixing versus return competition—affect blockchain security and agent incentives.
• To identify conditions under which staking pools enhance or undermine blockchain security and fairness.
• To establish the existence and uniqueness of equilibria in the staking pool formation game.
• To evaluate the impact of reward distribution rules on the share of honest versus malicious validators in the blockchain.

Proposed method

• Formalizes a game-theoretic model of staking pool formation with honest and malicious agents, where agents choose whether to run or delegate to pools.
• Models the blockchain as a mechanism where block proposers are selected proportionally to stake, with rewards distributed based on pool rules.
• Introduces two design mechanisms: return fixing (fixed split between pool owner and delegators) and return competition (pool owners compete on reward shares).
• Uses a continuum model with agents of infinitesimal measure to derive analytical conditions for equilibrium existence and uniqueness.
• Applies Chernoff concentration bounds to extend results to a discrete setting with finite, large numbers of agents.
• Derives a threshold condition on the reward share λ for the existence of a positive equilibrium, showing λ ≥ m/(n + m) is necessary when c* = 0.

Experimental results

Research questions

• RQ1 Under what conditions do staking pools exist and form stable equilibria in the presence of malicious agents?
• RQ2 How does return competition between pool owners affect blockchain security compared to return fixing?
• RQ3 What role does the cost of running a pool play in determining whether honest agents choose to form pools?
• RQ4 Can reward distribution rules be designed to prevent malicious agents from capturing disproportionate rewards?
• RQ5 How does the model’s continuum approximation compare to finite-agent discrete models in terms of equilibrium outcomes?

Key findings

• In the return fixing mechanism, no honest agent runs a pool in equilibrium, leading to blockchain disruption due to zero measure impact from individual actions.
• In the return competition mechanism, a unique equilibrium exists where honest agents form pools only if the reward share λ satisfies λ ≥ m/(n + m), ensuring positive participation.
• The model shows that allowing staking pools can increase returns for honest stakeholders but may reduce blockchain security if not properly governed.
• With welfare-optimized reward distribution, malicious agents are prevented from receiving large rewards, improving system resilience.
• The discrete model approximation confirms the continuum result, showing that the equilibrium condition is robust to finite agent counts under large n.
• The analysis reveals that return competition leads to better security outcomes than return fixing, as it aligns incentives and prevents free-riding by honest agents.