---
# System prepended metadata

title: Analysis of Centralization Patterns in Staking Agents

---

Analysis of Centralization Patterns in Staking Agents
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#ethereum #grant
## Project Abstract

The scope of the project is to analyse the centralisation pattern of consensus agents, focusing on the effects of Ethereum's transition to Proof-of-Stake. 
It has been observed and [theoretically described](https://arxiv.org/abs/1905.05158) that centralisation is naturally driven in the system by profit-seeking validators/miners. The emergence of centralisation of consensus resources poses a real threat to the core principles of Ethereum and to its viability as a blockchain, and, to a lesser threatening but very tangible way, it may enable censoriship behaviours on the blockchain.
The temporal evolution of stake centralization is hypothesized to be closely linked with the fairness of rewards, specifically whether rewards are proportional to stake and whether particular subsets of validators experience discrimination. To further explore these issues, insights derived from our data analysis will be incorporated into a simulation, capable of assessing the likelihood of censorship and predicting future stake evolution while considering its impact on centralization dynamics.
We believe a correct understanding of the current status of Ethereum consensus centralisation, and the driving forces behind it, with specific focus to the role of validation pools ( e.g.liquid staking phenomena as LIDO), will increase the ability of the Ethereum's eco-system to react and set the course for a healthy and sustainable development.


## Objectives

The goal of this project is to produce a scientific paper to be published in a peer-reviewed journal or in the proceedings of a relevant conference.
## Outcomes

We believe a complete an objective assesment from an independent party on the status of stakes distribution behind Ethereum validators may be beneficial in assessing the health of Ethereum consensus protocol and to keep Ethereum users informed.
## Grant Scope
The project consists of a data collection phase and an analysis phase.
We are going to combine data collected directly from the Ethereum blockchain in order to construct a reliable set of the stake temporal distribution in the period of time surrounding the Merge. Data from the miners' hasing power distribution on the PoW Ethereum network are going to be gathered for comparison.
Once the data collection phase is completed, we are going to analyse the data in order to study the effect on consensus-maintainance resources of the Proof-of-Stake transition, specifically the evolution of stake concentration.
We are particularly interested in the emergence and dynamics behind centralised validators pools(e.g. [Lido](https://lido.fi/), [Binance Staking](https://www.binance.com/en/eth2), etc.), and their role (and surge to promincence) in Ethereum consensus.
We will analyse the data along an economic reason of thinking and compare it to the situation before the Merge. 
Finally we will use the knowledge gathered in the previous research to adapt an agent-based model and simulate the dynamics of stake evolution and reward distributions and make a critical assessment of the future challenges for the Ethereum Network. 

## Project Team

- Claudio J. Tessone: Claudio J. Tessone is Professor of Blockchain and Distributed Ledger Technologies at the Informatics Department, University of Zurich. He is co-founder and Chairman of the UZH Blockchain Center. He holds a PhD in Physics (on complex systems) and a Habilitation on "Complex socio-economic systems" from ETH Zurich. He is an expert in the modeling of complex socio-economic, and socio-technical systems from an interdisciplinary perspective. He is interested in the link between microscopic agent behaviour and the rules these agents abide to, and the global, emergent properties of socio-economic and socio-technical systems. Blockchain-based systems and cryptocurrencies are the main pillar of his research (being among the first to study them). This includes cryptoeconomics (from financial aspects to meso- and macro- properties, such as withstanding, emergent centralization), big-data blockchain analytics and forensics, design of blockchain-based systems, and characterization of economic incentives that are present (by design or set inadvertently) in them. He is the director of the Summer School: Deep Dive into Blockchain and of the Certificate of Advanced Studies on Blockchain at the University of Zurich.
    - Professor Tessone is going to lead the research team, providing guidance and insight on the research design and results discussion.
- Nicolò Vallarano: Nicolò Vallarano fields of research range between the statistical mechanics of networks and distributed ledger technologies. His PhD thesis included an application of an improved version of the ERGM configuration model to the network of Bitcoin Users Transactions. At the moment he is collaborating with Prof. Claudio Tessone modeling consensus protocols other than the classic Bitcoin Proof-of-work. As part of his research activity he collaborates with the Blockchain Observatory in the study and classification of cryptocurrencies economic state.
    - Nicolo' vallarano is going to participate in the data collection and analysis, togheter with the paper writing.
- Benjamin Kraner: Benjamin Kraner is a PhD candidate at the University of Zurich. He holds a MA in Economics and is currently working on the modelling of incentives and Tokenomics in Blockchains and distributed ledger technologies systems.  
    - Benjamin Kraner will participate in the analysis and the final writing of the paper.

## Background
The Blockchain and Decentralised Ledger Technology group at the University of Zurich is a research group specialised in an inter-disciplinary approach to blockchain technology.
We already won a grant at the [Ethereum Academic Grants Rounds 2022](https://blog.ethereum.org/2022/07/29/academic-grants-grantee-announce) on the topic of consensus algorithm: we developed an agent-based model of Ethereum proof-of-stake consensus. The code is open source and currently available on [github](https://github.com/benckj/ethereum-consensus-abm), while the related paper is currently under submission at a scientific conference.

Here's a list of papers published by members of the group on blockchain-related topics:
- Vallarano, Nicoló, Claudio J. Tessone, and Tiziano Squartini. "Bitcoin Transaction Networks: an overview of recent results." Frontiers in Physics (2020): 286.
- Garcia, D., Tessone, C. J., Mavrodiev, P., & Perony, N. "The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy." Journal of the Royal Society Interface 11.99 (2014): 20140623. 
- Tasca, Paolo, and Claudio J. Tessone. "Taxonomy of blockchain technologies. Principles of identification and classification." arXiv preprint arXiv:1708.04872 (2017).
- Li, Sheng-Nan, Zhao Yang, and Claudio J. Tessone. "Proof-of-Work cryptocurrency mining: a statistical approach to fairness." 2020 IEEE/CIC International Conference on Communications in China (ICCC Workshops). IEEE, 2020.
- Fadda, Edoardo, Claudio J. Tessone and Paolo Barucca. "Consensus formation on heterogeneous networks." arXiv preprint arXiv:2111.11949 (2021).
- Tessone, Claudio, Paolo Tasca, and Flavio Iannelli. "Stochastic modelling of blockchain consensus." Available at SSRN 3865040 (2021).
- Schwarz-Schilling, Caspar, Sheng-Nan Li, and Claudio J. Tessone. "Agent-based Modelling of Strategic behavior in PoW Protocols." 2021 Third International Conference on Blockchain Computing and Applications (BCCA). IEEE, 2021.
- Li, Chuanyun, Florian Spychiger, and Claudio J. Tessone. "The Miner's Dilemma With Migration." 2021 3rd Conference on Blockchain Research & Applications for Innovative Networks and Services (BRAINS). IEEE, 2021.
- Kraner, Benjamin, Sheng-Nan Li, Andreia S. Teixeira and Claudio J Tessone. “Ultimatum Game of Mining in Blockchain Systems without Block Rewards” International School and Conference on Network Science (NetSciX 2022) 8-11 February 2022 Porto, Portugal
- Spychiger, Florian, Paolo Tasca, and Claudio J. Tessone. "Unveiling the importance and evolution of design components through the “tree of blockchain”." Frontiers in Blockchain 3 (2021): 60.

## Methodology

Our first objective is to establish a data collection pipeline that will allow us to gather information about the distribution of stakes and hashing power (pre-Merge).
To better understand the centralization of stakes, we will use established measures from scientific literature, such as the Herfindahl–Hirschman Index, Nakamoto Index, Shannon Entropy, and Gini Index. These measures will provide a comprehensive description of the level of centralization present in the system.
Another important aspect of our analysis is the examination of staking rewards and their fairness. By studying the allocation of staking rewards, we can determine if there are any issues with the distribution of these rewards and identify ways to improve fairness.
To simulate the impact of censorship and stake evolution in a simplified setting, we will utilize a [a state-of-the art agent based simulator](https://github.com/benckj/ethereum-consensus-abm). This simulator will help us gain insight from the data analysis part and enable us to better understand the system's response to different scenarios. Our chosen simulator is available on GitHub and is designed specifically for studying Ethereum consensus.


## Timeline

We expect the project to take up to 6 months to be completed. 
- Milestone 1 (2 months): Set up the staking resources data collection to aquire the hashing power distribution from web database.
- Milestone 2 (4 months): Publicly share a polished verison of the paper with data analsyis and theorical framework for model situation
- Milestone 3 (6 months): Paper submission to peer-rewieved journal and/or scientific conference of relevant field to the topic.

## Budget
We expect the project to take up to 6 months to be completed. A half-time PhD student (PHD) and a half-time senior research associate (PD) from UZH would work on the project. Grant funds would be used to pay the salary of the PhD and the research associate (the following salary estimates including social security and UZH overhead):
- 2 PhD student monthly salary at 50%: CHF 2822.4.
- Senior Research Associate monthly salary at 25%: CHF 2879.58.

Summing the salaries and multiplying by 6 months we obtain the budget request of CHF 51146.28. In addition to this, we consider CHF 2700 for conference fees and CHF 3750 for international travel to cover the expenses to present the paper at a major scientific conference, leading to a total of CHF 57596.28.
Software and Hardware cost will be covered using the university infrastructure. All the cost goes to pay the researchers.
