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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…

密码学与安全 · 计算机科学 2018-08-13 Fabian Ritz , Alf Zugenmaier

Bitcoin is a decentralized crypto-currency, and an accompanying protocol, created in 2008. Bitcoin nodes continuously generate and propagate blocks---collections of newly approved transactions that are added to Bitcoin's ledger. Block…

密码学与安全 · 计算机科学 2015-07-24 Ayelet Sapirshtein , Yonatan Sompolinsky , Aviv Zohar

Cryptocurrency is a well-developed blockchain technology application that is currently a heated topic throughout the world. The public availability of transaction histories offers an opportunity to analyze and compare different…

统计金融 · 定量金融 2018-08-28 Jiaqi Liang , Linjing Li , Daniel Zeng

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…

理论经济学 · 经济学 2020-04-21 Charles Bertucci , Louis Bertucci , Jean-Michel Lasry , Pierre-Louis Lions

Miners play a key role in cryptocurrencies such as Bitcoin: they invest substantial computational resources in processing transactions and minting new currency units. It is well known that an attacker controlling more than half of the…

密码学与安全 · 计算机科学 2019-05-16 Matteo Romiti , Aljosha Judmayer , Alexei Zamyatin , Bernhard Haslhofer

Sharding is used to improve the scalability and performance of blockchain systems. We investigate the stability of blockchain sharding, where transactions are continuously generated by an adversarial model. The system consists of $n$…

分布式、并行与集群计算 · 计算机科学 2024-04-23 Ramesh Adhikari , Costas Busch , Dariusz R. Kowalski

This paper integrates Austrian capital theory with repeated game theory to examine strategic miner behaviour under different institutional conditions in blockchain systems. It shows that when protocol rules are mutable, effective time…

综合经济学 · 经济学 2025-06-27 Craig Steven Wright

We propose a bitcoin generalization as a solution to the problem of scalability. The block is redefined as a sequence of sub-blocks of increasing sizes that coexist as different levels of compromise between decentralization and transactions…

密码学与安全 · 计算机科学 2018-05-15 Santi J. Vives

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…

分布式、并行与集群计算 · 计算机科学 2019-02-22 Yackolley Amoussou-Guenou , Bruno Biais , Maria Potop-Butucaru , Sara Tucci-Piergiovanni

We study Nash-dynamics in the context of blockchain protocols. We introduce a formal model, within which one can assess whether the Nash dynamics can lead utility-maximizing participants to defect from the "honest" protocol operation,…

密码学与安全 · 计算机科学 2022-03-24 Dimitris Karakostas , Aggelos Kiayias , Thomas Zacharias

Proof-of-Stake blockchains based on a longest-chain consensus protocol are an attractive energy-friendly alternative to the Proof-of-Work paradigm. However, formal barriers to "getting the incentives right" were recently discovered, driven…

计算机科学与博弈论 · 计算机科学 2023-10-31 Matheus V. X. Ferreira , S. Matthew Weinberg

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader…

计算机科学与博弈论 · 计算机科学 2026-03-26 Sam Ganzfried

The security of Bitcoin protocols is deeply dependent on the incentives provided to miners, which come from a combination of block rewards and transaction fees. As Bitcoin experiences more halving events, the protocol reward converges to…

密码学与安全 · 计算机科学 2025-09-12 Roozbeh Sarenche , Alireza Aghabagherloo , Svetla Nikova , Bart Preneel

One of the most important features of blockchain protocols is decentralization, as their main contribution is that they formulate a distributed ledger that will be maintained and extended without the need of a trusted party. Bitcoin has…

密码学与安全 · 计算机科学 2023-07-25 Aikaterini-Panagiota Stouka , Thomas Zacharias

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.…

计算机科学与博弈论 · 计算机科学 2021-07-21 Alejandro Jofré , Angel Pardo , David Salas , Victor Verdugo , José Verschae

Popular distributed ledger technology (DLT) systems using proof-of-work (PoW) for Sybil attack resistance have extreme energy requirements, drawing stern criticism from academia, businesses, and the media. DLT systems building on…

分布式、并行与集群计算 · 计算机科学 2022-04-05 Moritz Platt , Johannes Sedlmeir , Daniel Platt , Paolo Tasca , Jiahua Xu , Nikhil Vadgama , Juan Ignacio Ibañez

Proof-of-Work (PoW) is a popular consensus protocol used by Bitcoin since its inception. PoW has the well-known flaw of assigning all the reward to the single miner (or pool) that inserts the new block. This has the consequence of making…

分布式、并行与集群计算 · 计算机科学 2022-07-13 Danilo Bazzanella , Andrea Gangemi

The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth…

密码学与安全 · 计算机科学 2019-11-25 Erica Blum , Aggelos Kiayias , Cristopher Moore , Saad Quader , Alexander Russell

The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many…

物理与社会 · 物理学 2022-04-06 Natalia L. Kontorovsky , Juan Pablo Pinasco , Federico Vazquez

The resource-consuming mining of blocks on a blockchain equipped with a proof of work consensus protocol bears the risk of ruin, namely when the operational costs for the mining exceed the received rewards. In this paper we investigate to…

密码学与安全 · 计算机科学 2021-09-08 Hansjoerg Albrecher , Dina Finger , Pierre-Olivier Goffard