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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

Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community. We provide an explanation using a simple model to…

Cryptography and Security · Computer Science 2018-11-22 Nick Arnosti , S. Matthew Weinberg

We model and analyze blockchain miners who seek to maximize the compound return of their mining businesses. The analysis of the optimal strategies finds a new equilibrium point among the miners and the mining pools, which predicts the…

Cryptography and Security · Computer Science 2020-12-07 Go Yamamoto , Aron Laszka , Fuhito Kojima

Blockchain systems often employ proof-of-work consensus protocols to validate and add transactions into hashchains. These protocols stimulate competition among miners in solving cryptopuzzles (e.g. SHA-256 hash computation in Bitcoin) in…

Computer Science and Game Theory · Computer Science 2020-05-13 Venkata Sriram Siddhardh Nadendla , Lav R. Varshney

Bitcoin-NG, a scalable blockchain protocol, divides each block into a key block and many micro blocks to effectively improve the transaction processing capacity. Bitcoin-NG has a special incentive mechanism (i.e. splitting transaction fees…

Cryptography and Security · Computer Science 2020-06-23 Taotao Wang , Xiaoqian Bai , Hao Wang , Soung Chang Liew , Shengli Zhang

All public blockchains are secured by a proof of opportunity cost among block producers. For example, the security offered by proof-of-work (PoW) systems, like Bitcoin, is due to spent computation; it is work precisely because it cannot be…

Computer Science and Game Theory · Computer Science 2019-08-27 George Bissias , Brian N. Levine , David Thibodeau

Mining blocks in a blockchain using the \textit{Proof-of-Work} consensus protocol involves significant risk, as network participants face continuous operational costs while earning infrequent capital gains upon successfully mining a block.…

Cryptography and Security · Computer Science 2025-11-19 Pierre-Olivier Goffard , Hansjoerg Albrecher , Jean-Pierre Fouque

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

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

Many of today's crypto currencies use blockchains as decentralized ledgers and secure them with proof of work. In case of a fork of the chain, Bitcoin's rule for achieving consensus is selecting the longest chain and discarding the other…

Cryptography and Security · Computer Science 2018-08-13 Fabian Ritz , Alf Zugenmaier

Blockchain-based cryptocurrencies secure a decentralized consensus protocol by incentives. The protocol participants, called miners, generate (mine) a series of blocks, each containing monetary transactions created by system users. As…

Cryptography and Security · Computer Science 2018-11-14 Itay Tsabary , Ittay Eyal

Mining for Bitcoins is a high-risk high-reward activity. Miners, seeking to reduce their variance and earn steadier rewards, collaborate in pooling strategies where they jointly mine for Bitcoins. Whenever some pool participant is…

Computer Science and Game Theory · Computer Science 2017-03-14 Ben A. Fisch , Rafael Pass , Abhi Shelat

Selfish miners selectively withhold blocks to earn disproportionately high revenue. The vast majority of the selfish mining literature focuses exclusively on block rewards. Carlsten et al. [2016] is a notable exception, observing that…

Computer Science and Game Theory · Computer Science 2025-08-11 Maryam Bahrani , Michael Neuder , S. Matthew Weinberg

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 fairness in blockchain refers to equality between the computational resources invested in mining and the block rewards received. There exists a dilemma wherein increasing the transaction processing capacity of a blockchain…

Cryptography and Security · Computer Science 2025-09-10 Akira Sakurai , Kazuyuki Shudo

In blockchain networks adopting the proof-of-work schemes, the monetary incentive is introduced by the Nakamoto consensus protocol to guide the behaviors of the full nodes (i.e., block miners) in the process of maintaining the consensus…

Computer Science and Game Theory · Computer Science 2018-01-01 Xiaojun Liu , Wenbo Wang , Dusit Niyato , Narisa Zhao , Ping Wang

Bitcoin-NG is an extensible blockchain protocol based on the same trust model as Bitcoin. It divides each epoch into one Key-Block and multiple Micro-Blocks, effectively improving transaction processing capacity. Bitcoin-NG adopts a special…

Cryptography and Security · Computer Science 2023-06-07 Junjie Hu , Zhe Jiang , Chunxiang Xu

We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational…

Optimization and Control · Mathematics 2022-01-25 Zongxi Li , A. Max Reppen , Ronnie Sircar

The arisen of Bitcoin has led to much enthusiasm for blockchain research and block mining, and the extensive existence of mining pools helps its participants (i.e., miners) gain reward more frequently. Recently, the mining pools are proved…

Computer Science and Game Theory · Computer Science 2020-08-18 Zhihuai Chen , Bo Li , Xiaohan Shan , Xiaoming Sun , Jialin Zhang

The goal of this paper is to establish the general framework of consensus equilibria for Mining-Pool Games in Blockchain Ecosystems, and with the explanation for the stability of in terms of the existence of consensus equilibria related to…

Cryptography and Security · Computer Science 2020-07-01 George Yuan
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