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We present an analysis of the Proof-of-Work consensus algorithm, used on the Bitcoin blockchain, using a Mean Field Game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted…

Theoretical Economics · Economics 2020-04-21 Charles Bertucci , Louis Bertucci , Jean-Michel Lasry , Pierre-Louis Lions

Mining blocks on a blockchain equipped with a proof of work consensus protocol is well-known to be resource-consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining, and is compensated by a…

Cryptography and Security · Computer Science 2020-10-27 Hansjoerg Albrecher , Pierre-Olivier Goffard

A decade long thrive of cryptocurrency has shown its potential as a source of alternative-finance and the security and the robustness of the underpinning blockchain technology. However, most cryptocurrencies fail to show inimitability and…

Cryptography and Security · Computer Science 2020-03-24 Yibin Xu , Yangyu Huang , Jianhua Shao

As the cornerstone of blockchain, block synchronization plays a vital role in maintaining the security. Without full blockchain synchronization, unexpected forks will emerge and thus providing a breeding ground for various malicious…

Emerging Technologies · Computer Science 2022-06-14 Qin Hu , Minghui Xu , Shengling Wang , Shaoyong Guo

In this paper we discuss Bitcoin, the leader among the existing cryptocurrencies, to analyse its trends, success factors, current challenges and probable solutions to make it even better. In the introduction section, we discuss the history…

Cryptography and Security · Computer Science 2014-12-24 Siddharth Prakash Rao

Cryptocurrencies such as Bitcoin are realized using distributed systems and hence critically rely on the performance and security of the interconnecting network. The requirements on these networks and their usage, however can differ…

Networking and Internet Architecture · Computer Science 2020-08-20 Maya Dotan , Yvonne-Anne Pignolet , Stefan Schmid , Saar Tochner , Aviv Zohar

Cryptocurrency, the most controversial and simultaneously the most interesting asset, has attracted many investors and speculators in recent years. The visibly significant market capitalization of cryptos also motivates modern financial…

Risk Management · Quantitative Finance 2021-12-10 Junjie Hu , Wolfgang Karl Härdle , Weiyu Kuo

In a PoW-based blockchain network, mining pools (the solo miner could be regarded as a mining pool containing one miner) compete to successfully mine blocks to pursue rewards. Generally, the rewards include the fixed block subsidies and…

Computer Science and Game Theory · Computer Science 2021-10-20 Jinmian Chen , Yukun Cheng , Zhiqi Xu , Yan Cao

Over the past decade, the blockchain technology and its Bitcoin cryptocurrency have received considerable attention. Bitcoin has experienced significant price swings in daily and long-term valuations. In this paper, we propose a partial…

Pricing of Securities · Quantitative Finance 2020-08-26 Yufang Wang , Haiyan Wang

Bitcoin has emerged as a fascinating phenomenon of the financial markets. Without any central authority issuing the currency, it has been associated with controversy ever since its popularity and public interest reached high levels. Here,…

Computational Finance · Quantitative Finance 2018-10-30 Ladislav Kristoufek

Bitcoin derives a verifiable temporal order from probabilistic block discovery and cumulative proof-of-work rather than from a trusted global clock. We show that block arrivals exhibit stable exponential behavior across difficulty epochs,…

Information Theory · Computer Science 2026-02-11 Bin Chen , Pan Feng

The world economy is experiencing the novel adoption of distributed currencies that are free from the control of central banks. Distributed currencies suffer from extreme volatility, and this can lead to catastrophic implications during…

Cryptography and Security · Computer Science 2022-06-22 Jacques Bou Abdo , Shuvalaxmi Dass , Basheer Qolomany , Liaquat Hossain

We make several contributions that quantify the real-time hash rate and therefore the consensus of a blockchain. We show that by using only the hash value of blocks, we can estimate and measure the hash rate of all miners or individual…

Cryptography and Security · Computer Science 2017-07-04 A. Pinar Ozisik , George Bissias , Brian Levine

Bitcoin constructs temporal order internally rather than synchronizing to any external clock. Empirical evidence shows that its time evolution is non-continuous, probabilistic, and self-regulated. Block discovery follows a stochastic…

Cryptography and Security · Computer Science 2025-11-20 Bin Chen

The security of blockchain systems is fundamentally based on the decentralized consensus in which the majority of parties behave honestly, and the content verification process is essential to maintaining the robustness of blockchain…

Cryptography and Security · Computer Science 2025-08-21 Zishuo Zhao , Xi Chen , Yuan Zhou

We investigate the relationship between underlying blockchain mechanism of cryptocurrencies and its distributional characteristics. In addition to price, we emphasise on using actual block size and block time as the operational features of…

Cryptography and Security · Computer Science 2021-08-25 Min-Bin Lin , Kainat Khowaja , Cathy Yi-Hsuan Chen , Wolfgang Karl Härdle

Smart contracts are stateful programs deployed on blockchains; they secure over a trillion dollars in transaction value per year. High-stakes smart contracts often rely on timely alerts about external events, but prior work has not analyzed…

Cryptography and Security · Computer Science 2026-04-14 Marwa Mouallem , Lorenz Breidenbach , Ittay Eyal , Ari Juels

The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75\% of total market capitalisation and compare their evolution with that of a…

Statistical Finance · Quantitative Finance 2023-09-08 Esther Cabezas-Rivas , Felipe Sánchez-Coll , Isaac Tormo-Xaixo

We study financial transaction confirmation finality in Bitcoin as a function of transaction amount and user risk tolerance. A transaction is recorded in a block on a blockchain. However, a transaction may be revoked due to a fork in the…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-20 Ethan Hicks , Joseph Oglio , Mikhail Nesterenko , Gokarna Sharma

Open-access blockchains based on proof-of-work protocols have gained tremendous popularity for their capabilities of providing decentralized tamper-proof ledgers and platforms for data-driven autonomous organization. Nevertheless, the…

Cryptography and Security · Computer Science 2019-05-14 Shaohan Feng , Wenbo Wang , Zehui Xiong , Dusit Niyato , Ping Wang , Shaun Shuxun Wang