Balancing Participation and Decentralization in Proof-of-Stake Cryptocurrencies

TL;DR

This work investigates how to balance participation, decentralization, and expenditure in PoS blockchains through stake delegation. It introduces a formal delegation game with uniform delegation rewards and a Bayesian extension, deriving sufficient conditions for equilibria and defining metrics for participation, decentralization, and expenditure. The authors develop a computational framework to evaluate ex post equilibria under stochastic agent types and demonstrate how different reward structures shape system behavior. The results reveal clear tradeoffs and show how payment schemes can be tuned to prioritize specific objectives while acknowledging potential costs to others. Overall, the paper provides a principled, multi-objective approach to designing delegation incentives that promote resilient, decentralized PoS ecosystems.

Abstract

Proof-of-stake blockchain protocols have emerged as a compelling paradigm for organizing distributed ledger systems. In proof-of-stake (PoS), a subset of stakeholders participate in validating a growing ledger of transactions. For the safety and liveness of the underlying system, it is desirable for the set of validators to include multiple independent entities as well as represent a non-negligible percentage of the total stake issued. In this paper, we study a secondary form of participation in the transaction validation process, which takes the form of stake delegation, whereby an agent delegates their stake to an active validator who acts as a stake pool operator. We study payment schemes that reward agents as a function of their collective actions regarding stake pool operation and delegation. Such payment schemes serve as a mechanism to incentivize participation in the validation process while maintaining decentralization. We observe natural trade-offs between these objectives and the total expenditure required to run the relevant payment schemes. Ultimately, we provide a family of payment schemes which can strike different balances between these competing objectives at equilibrium in a Bayesian game theoretic framework.

Figures (16)

• Figure 1: This Figure provides a breakdown of participation for the baseline parameter setting. Each point in the left plot is one of the 496 draws of types in the Bayesian PNE that gave rise to ex post SPO stability. The axes represent the relative proportion of stake that is used for delegation and SPO pledges. As we can see, all points lie on a line indicative of the fact that for no draw do we see idle agents. The right bar chart provides average values of absolute stake used by agents being idle, delegators or SPOs respectively.
• Figure 2: The top two plots provide insight regarding the spread of values the decentralization and expenditure objectives can take for ex post PNE in the baseline parameter setting. The $x$-axis for both of these plots corresponds to different representative PNE as per Algorithm \ref{['alg:greedy-delegation']}, in which the defining characteristic of a representative PNE is the reference pledge $\bar{\lambda}_j$, which is a proportional value relative to the spread of SPO pledges. The bottom graph simultaneously plots the performance of each representative ex post PNE in terms of decentralization and expenditure.
• Figure 3: This Figure provides a breakdown of participation as $\epsilon$ varies in $\{0.005,0.01,0.02,0.05\}$. Different $\epsilon$ values to different colors and each point in the plot corresponds to draws of types that gave rise to ex post SPO stability. The axes represent the relative proportion of stake that is used for delegation and SPO pledges. The right bar chart provides average values of absolute stake used by agents being idle, delegators or SPOs respectively for different threshold values.
• Figure 4: The top two plots provide insight regarding the spread of values the decentralization and expenditure objectives can take for ex post PNE $\epsilon$ values vary in $\{0.005,0.01,0.02,0.05\}$. The $x$ axis for both of these plots correspond to different representative PNE as per Algorithm \ref{['alg:greedy-delegation']}, in which the defining characteristic of a representative PNE is the reference pledge $\bar{\lambda}_j$, which is a proportional value relative to the spread of SPO pledges. The bottom graph simultaneously plots the performance of each representative ex post PNE in terms of decentralization and expenditure.
• Figure 5: This Figure provides a breakdown of participation as $a$ and $b$ vary in $\{g_1,\dots,g_6\}$. The first row corresponds to unilaterally modulating $a$, the second row corresponds to unilaterally modulating $b$, and the third row corresponds to modulating $(a,b) \in \{(g_1,g_1),\dots,(g_6,g_6)\}$. For each row, the left image is scatter plot where each point of a given color is an ex post PNE for a given $\rho$ function. For each row, the right image corresponds to the spread of absolute participation of each type (idle, delegation, SPO) for a given $\rho$ function.

Theorems & Definitions (29)

• Definition 1: Active-Inactive Pool
• Definition 2: The Delegation Game
• Definition 3: Pool Reward Function
• Definition 4: Capped Separable Pool Reward Function
• Definition 5
• Definition 6: Pool feasibility
• Definition 7: Uniform Delegation Agent Rewards
• Definition 8
• Definition 9: Max-delegate $r$
• Definition 10