Decentralization Analysis of Pooling Behavior in Cardano Proof of Stake

Blockchain protocols’ main differentiator is their purported decentralization that unlocks various information technology applications that were supposedly impossible beforehand. The key promise is that incentive-driven participation of a large set of interested parties can lead to decentralized protocol states where no single operator can be a “single point of failure.” Despite this promise, there is little systematic analysis of decentralization in blockchain systems and the sporadic theoretic and empirical investigations that exist paint a rather negative picture due to resource “pooling behaviors” that are impossible to prevent in the “permissionless” setting of such protocols where parties have no designated identities. Motivated by this, in this paper we study the Nash dynamics of pooling in the context of Proof of Stake systems, following an agent-based modeling approach. Our focus is the Cardano blockchain as it features a number of attractive characteristics making it conducive to an in-depth analysis. We aim to answer the question of whether the incentive mechanism employed is capable of promoting decentralization. To this end, we present a simulation engine that enables strategic agents to engage in a number of actions empirically observed in the real-world deployment of the system. The engine simulates the “stake pool operation and delegation game" via successive agent actions that improve their utility as more information about their environment becomes evident in the course of the simulation. We investigate convergence to equilibrium states, and we measure various decentralization metrics in these states, such as the Nakamoto coefficient, which asks how many independent entities exist that collectively command more than of the system’s resources. Our results exemplify the ability of the incentive mechanism to steer the system towards good equilibria and also illustrate how the decentralization features of such equilibria are affected by different choices of the parameters used in the mechanism and the distribution of stake to participants.