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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

Blockchains have recently gained popularity thanks to their ability to record "digital truth". They are designed to keep persistence, security, and avoid attacks which is useful for many applications. However, they are still problematic in…

Cryptography and Security · Computer Science 2019-01-14 David Amar , Lior Zilpa

Play-to-earn is one of the prospective categories of decentralized applications. The play-to-earn projects combine blockchain technology with entertaining games and finance, attracting various participants. While huge amounts of capital…

Cryptography and Security · Computer Science 2022-11-03 Jingfan Yu , Mengqian Zhang , Xi Chen , Zhixuan Fang

This paper presents a novel staking coopetition design aimed at incentivizing decentralization and continuous growth of economic security within a proof-of-stake system. Staking rewards follow a nonlinear mapping relative to stake size.…

Theoretical Economics · Economics 2025-05-19 Michael D. Norman , Simon Brown , Mallesh Pai , Laurence Smith

This paper proposes a conceptual framework for the analysis of reward sharing schemes in mining pools, such as those associated with Bitcoin. The framework is centered around the reported shares in a pool instead of agents and results in…

Computer Science and Game Theory · Computer Science 2021-07-13 Burak Can , Jens Leth Hougaard , Mohsen Pourpouneh

The widespread adoption of blockchain technology has amplified the spectrum of potential threats to its integrity and security. The ongoing quest to exploit vulnerabilities emphasizes how critical it is to expand on current research…

Cryptography and Security · Computer Science 2024-04-30 Kaustubh Dwivedi , Ankit Agrawal , Ashutosh Bhatia , Kamlesh Tiwari

Proof-of-work blockchains reward each miner for one completed block by an amount that is, in expectation, proportional to the number of hashes the miner contributed to the mining of the block. Is this proportional allocation rule optimal?…

Computer Science and Game Theory · Computer Science 2019-09-25 Xi Chen , Christos Papadimitriou , Tim Roughgarden

Motivated by emerging decentralized applications, the \emph{game of coding} framework has been recently introduced to address scenarios where the adversary's control over coded symbols surpasses the fundamental limits of traditional coding…

Information Theory · Computer Science 2025-02-12 Hanzaleh Akbarinodehi , Parsa Moradi , Mohammad Ali Maddah-Ali

A blockchain faces two fundamental challenges. It must motivate users to maintain the system while preventing a minority of these users from colluding and gaining disproportionate control. Many popular public blockchains use monetary…

Cryptography and Security · Computer Science 2021-10-15 Shea Ketsdever , Michael J. Fischer

Our aim in this paper is to investigate the profitability of double-spending (DS) attacks that manipulate an a priori mined transaction in a blockchain. It was well understood that a successful DS attack is established when the proportion…

Cryptography and Security · Computer Science 2020-10-15 Jehyuk Jang , Heung-No Lee

Bitcoin mining presents a significant economic incentive for efficient hashing and broadcast of data, both parameters stemming from the Proofs of Work used to advance the network. This incentive has led to the development of Bitcoin…

Cryptography and Security · Computer Science 2016-03-17 Jonathan Harvey-Buschel , Can Kisagun

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

Credit allows a lender to loan out surplus capital to a borrower. In the traditional economy, credit bears the risk that the borrower may default on its debt, the lender hence requires upfront collateral from the borrower, plus interest fee…

Cryptography and Security · Computer Science 2021-03-23 Kaihua Qin , Liyi Zhou , Benjamin Livshits , Arthur Gervais

Researchers have discovered a series of theoretical attacks against Bitcoin's Nakamoto consensus; the most damaging ones are selfish mining, double-spending, and consistency delay attacks. These attacks have one common cause: block…

Cryptography and Security · Computer Science 2023-12-04 Jianyu Niu , Fangyu Gai , Runchao Han , Ren Zhang , Yinqian Zhang , Chen Feng

Recently, two attacks were presented against Proof-of-Stake (PoS) Ethereum: one where short-range reorganizations of the underlying consensus chain are used to increase individual validators' profits and delay consensus decisions, and one…

Cryptography and Security · Computer Science 2021-10-20 Caspar Schwarz-Schilling , Joachim Neu , Barnabé Monnot , Aditya Asgaonkar , Ertem Nusret Tas , David Tse

Blockchain systems benefit from lessons in prior art such as fault tolerance, distributed systems, peer-to-peer systems, and game theory. In this paper we argue that blockchain algorithms should tolerate both rational (self-interested)…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-11-05 Jean-Philippe Martin , Eunjin , Jung

We develop a model of coordination and allocation of decentralized multi-sided markets, in which our theoretical analysis is promisingly optimizing the decentralized transaction packaging process at high-throughput blockchains or Web 3.0…

General Economics · Economics 2023-01-27 Yuxuan Lu , Qian Qi , Xi Chen

Blockchain consensus is a state whereby each node in a network agrees on the current state of the blockchain. Existing protocols achieve consensus via a contest or voting procedure to select one node as a dictator to propose new blocks.…

Theoretical Economics · Economics 2022-06-22 Joshua S. Gans , Richard Holden

As an emerging service framework built by combining cryptography, P2P network, consensus mechanism and innovative contract technology, blockchain has been widely used in digital finance, data sharing, message traceability and electronic…

Cryptography and Security · Computer Science 2025-08-05 Wenwen Zhou , Dongyang Lyu , Xiaoqi Li

We study selfish mining in Ethereum. The problem is combinatorially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula. Equivalent strategies in Bitcoin do have…

Cryptography and Security · Computer Science 2019-05-01 Cyril Grunspan , Ricardo Pérez-Marco