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Cooperation is fundamental for human prosperity. Blockchain, as a trust machine, is a cooperative institution in cyberspace that supports cooperation through distributed trust with consensus protocols. While studies in computer science…

General Economics · Economics 2023-01-23 Luyao Zhang , Xinyu Tian

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

A decentralized blockchain is a distributed ledger that is often used as a platform for exchanging goods and services. This ledger is maintained by a network of nodes that obeys a set of rules, called a consensus protocol, which helps to…

Optimization and Control · Mathematics 2022-01-03 Lucy Klinger , Lei Zhang , Zhennan Zhou

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

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

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

Blockchain plays a crucial role in ensuring the security and integrity of decentralized systems, with the proof-of-work (PoW) mechanism being fundamental for achieving distributed consensus. As PoW blockchains see broader adoption, an…

Systems and Control · Electrical Eng. & Systems 2026-01-07 Xunqiang Lan , Xiao Tang , Ruonan Zhang , Bin Li , Qinghe Du , Dusit Niyato , Zhu Han

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

Blockchains have witnessed widespread adoption in the past decade in various fields. The growing demand makes their scalability and sustainability challenges more evident than ever. As a result, more and more blockchains have begun to adopt…

Computer Science and Game Theory · Computer Science 2021-07-12 Shashank Motepalli , Hans-Arno Jacobsen

Blockchain technology is a breakthrough in changing the ways of business and organization operations, in which the consensus problem is challenging with practical constraints, such as computational power and consensus standard. In this…

Computational Engineering, Finance, and Science · Computer Science 2023-09-19 Yuqi Xie , Changbing Tang , Feilong Lin , Guanrong Chen , Zhao Zhang , Zhonglong Zheng

Blockchains rely on economic incentives to ensure secure and decentralised operation, making incentive compatibility a core design concern. However, protocols are rarely deployed in isolation. Applications interact with the underlying…

Computer Science and Game Theory · Computer Science 2026-04-08 Zeta Avarikioti , Georg Fuchsbauer , Pim Keer , Matteo Maffei , Fabian Regen

In 2015, Eyal proposed the first game-theoretical model for analyzing the equilibrium of blockchain pooling: when the blockchain pools are abstracted as a non-cooperative game, two pools can reach a Nash equilibrium with a closed-form…

Cryptography and Security · Computer Science 2020-05-06 Dongfang Zhao

The energy sustainability of blockchains, whose consensus protocol rests on the Proof-of-Work, nourishes a heated debate. The underlying issue lies in a highly energy-consuming process, defined as mining, required to validate crypto-asset…

To maintain blockchain-based services with ensuring its security, it is an important issue how to decide a mining reward so that the number of miners participating in the mining increases. We propose a dynamical model of decision-making for…

Computer Science and Game Theory · Computer Science 2022-04-13 Kosuke Toda , Naomi Kuze , Toshimitsu Ushio

Understanding the strategic behavior of miners in a blockchain is of great importance for its proper operation. A common model for mining games considers an infinite time horizon, with players optimizing asymptotic average objectives.…

Computer Science and Game Theory · Computer Science 2021-07-21 Alejandro Jofré , Angel Pardo , David Salas , Victor Verdugo , José Verschae

This position paper presents a synthesis viewpoint of blockchains from two orthogonal perspectives: fault-tolerant distributed systems and game theory. Specifically, we formulate a new game-theoretical problem in the context of blockchains…

Artificial Intelligence · Computer Science 2019-12-23 Dongfang Zhao

We present a novel framework for analyzing blockchain consensus mechanisms by modeling blockchain growth as a Partially Observable Stochastic Game (POSG) which we reduce to a set of Partially Observable Markov Decision Processes (POMDPs)…

Computer Science and Game Theory · Computer Science 2026-01-12 Yanni Georghiades , Takashi Tanaka , Sriram Vishwanath

In this paper we analyze from the game theory point of view Byzantine Fault Tolerant blockchains when processes exhibit rational or Byzantine behavior. Our work is the first to model the Byzantine-consensus based blockchains as a committee…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-22 Yackolley Amoussou-Guenou , Bruno Biais , Maria Potop-Butucaru , Sara Tucci-Piergiovanni

We study a game-theoretic model of blockchain mining economies and show that griefing, a practice according to which participants harm other participants at some lesser cost to themselves, is a prevalent threat at its Nash equilibria. The…

Computer Science and Game Theory · Computer Science 2021-06-24 Yun Kuen Cheung , Stefanos Leonardos , Georgios Piliouras , Shyam Sridhar

Blockchain-based consensus protocols present the opportunity to develop new protocols, due to their novel requirements of open participation and explicit incentivization of participants. To address the first requirement, it is necessary to…

Cryptography and Security · Computer Science 2018-08-09 Sarah Azouvi , Patrick McCorry , Sarah Meiklejohn
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