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In this paper we describe the various scoring systems used to calculate rewards of participants in Bitcoin pooled mining, explain the problems each were designed to solve and analyze their respective advantages and disadvantages.

Distributed, Parallel, and Cluster Computing · Computer Science 2011-12-22 Meni Rosenfeld

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

Blockchain is rapidly emerging as an important class of network application, with a unique set of trust, security and transparency properties. In a blockchain system, participants record and update the `server-side' state of an application…

Networking and Internet Architecture · Computer Science 2022-05-24 Yifan Mao , Shaileshh Bojja Venkatakrishnan

Reward models are crucial for aligning large language models (LLMs) with human values and intentions. Existing approaches follow either Generative (GRMs) or Discriminative (DRMs) paradigms, yet both suffer from limitations: GRMs typically…

Computation and Language · Computer Science 2026-03-03 Longze Chen , Lu Wang , Renke Shan , Ze Gong , Run Luo , Jiaming Li , Jing Luo , Qiyao Wang , Min Yang

Forks in the Bitcoin network result from the natural competition in the blockchain's Proof-of-Work consensus protocol. Their frequency is a critical indicator for the efficiency of a distributed ledger as they can contribute to resource…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-11-18 Paolo Barucca , Carlo Campajola , Jiahua Xu

An important feature of Proof-of-Work (PoW) blockchains is full dynamic availability, allowing miners to go online and offline while requiring only 50% of the online miners to be honest. Existing Proof-of-stake (PoS), Proof-of-Space and…

Cryptography and Security · Computer Science 2021-02-22 Soubhik Deb , Sreeram Kannan , David Tse

We analyze the economic incentives generated by the proof-of-stake mechanism discussed in the Ethereum Casper upgrade proposal. Compared with proof-of-work, proof-of-stake has a different cost structure for attackers. In Budish (2018),…

Cryptography and Security · Computer Science 2018-07-26 George Gui , Ali Hortacsu , Jose Tudon

This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…

Optimization and Control · Mathematics 2026-04-23 Simone Baroncini , Bahman Gharesifard , Giuseppe Notarstefano

As cryptographic tokens and altcoins are increasingly being built to serve as utility tokens, the notion of useful work consensus protocols, as opposed to number-crunching PoW consensus, is becoming ever more important. In such contexts,…

Cryptography and Security · Computer Science 2019-05-13 Michał Król , Alberto Sonnino , Mustafa Al-Bassam , Argyrios Tasiopoulos , Ioannis Psaras

Bitcoin is the most successful cryptocurrency so far. This is mainly due to its novel consensus algorithm, which is based on proof-of-work combined with a cryptographically-protected data structure and a rewarding scheme that incentivizes…

Cryptography and Security · Computer Science 2019-05-24 Pawel Szalachowski , Daniel Reijsbergen , Ivan Homoliak , Siwei Sun

Inference-time scaling methods rely on Process Reward Models (PRMs), which are often poorly calibrated and overestimate success probabilities. We propose, to our knowledge, the first use of conditional optimal transport for calibrating…

Machine Learning · Computer Science 2026-05-13 Rachel Ma , Dylan Hadfield-Menell , Kristjan Greenewald

Bitcoin mining is a wasteful and resource-intensive process. To add a block of transactions to the blockchain, miners spend a considerable amount of energy. The Bitcoin protocol, named 'proof of work' (PoW), resembles a lottery and the…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-01-28 Andrei Lihu , Jincheng Du , Igor Barjaktarevic , Patrick Gerzanics , Mark Harvilla

Regardless of their variations, blockchains require a consensus mechanism to validate transactions, supervise added blocks, maintain network security, synchronize the network state, and distribute incentives. Proof-of-Work (PoW), one of the…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-25 Amirreza Sokhankhosh , Sara Rouhani

Most concurrent blockchain systems rely heavily on the Proof-of-Work (PoW) or Proof-of-Stake (PoS) mechanisms for decentralized consensus and security assurance. However, the substantial energy expenditure stemming from computationally…

Cryptography and Security · Computer Science 2026-05-05 Zishuo Zhao , Zhixuan Fang , Xuechao Wang , Xi Chen , Hongxu Su , Haibo Xiao , Yuan Zhou

This paper presents a comprehensive comparative analysis of two dominant blockchain consensus mechanisms, Proof of Work (PoW) and Proof of Stake (PoS), evaluated across seven critical metrics: energy use, security, transaction speed,…

Cryptography and Security · Computer Science 2025-11-24 Kaeli Andrews , Linh B. Ngo , Md Amiruzzaman

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

Does the proof-of-work protocol serve its intended purpose of supporting decentralized cryptocurrency mining? To address this question, we develop a game-theoretical model where miners first invest in hardware to improve the efficiency of…

Trading and Market Microstructure · Quantitative Finance 2021-06-21 Agostino Capponi , Sveinn Olafsson , Humoud Alsabah

We consider the problem of fair allocation of indivisible items among $n$ agents with additive valuations, when agents have equal entitlements to the goods, and there are no transfers. Best-of-Both-Worlds (BoBW) fairness mechanisms aim to…

Computer Science and Game Theory · Computer Science 2022-03-25 Moshe Babaioff , Tomer Ezra , Uriel Feige

Bitcoin's Proof of Work (PoW) mechanism, while central to achieving decentralized consensus, has long been criticized for excessive energy use and hardware inefficiencies \cite{devries2018bitcoin, truby2018decarbonizing}. This paper…

Cryptography and Security · Computer Science 2025-08-19 Mohammad Ishzaz Asif Rafid , Morsalin Sakib

Bitcoin uses blockchain technology and proof-of-work (PoW) mechanism where nodes spend computing resources and earn rewards in return for spending these resources. This incentive system has caused power to be significantly biased towards a…

Cryptography and Security · Computer Science 2019-09-04 Yujin Kwon , Jian Liu , Minjeong Kim , Dawn Song , Yongdae Kim