A novel hybrid share reporting strategy for blockchain miners in PPLNS pools
Introduction
Since the blockchain technology was invented in Bitcoin by Satoshi Nakamoto [10], blockchain mining has attracted a lot of participants to compete for the lucrative cryptocurrency rewards through contributing their computational power to the blockchain network [8,9,25]. Due to the desirable characteristics of the blockchain technology, it has raised many researchers' interests [1,6,21], and has been applied in many fields with success so far [3,17,20,22,27].
In blockchain mining, miners compete to solve the proof-of-work (PoW) based cryptographic puzzles with their computational power, and only the winning miner can create the next block and get the cryptocurrency reward, if the new block can be appended onto the blockchain ledger [18]. Since the cryptocurrency reward is extremely lucrative, blockchain mining has attracted more and more miners swarming into this new market, resulting in a sharp increase in the difficulty of finding new blocks. As such, miners may find it even harder to find a new block using the so-called solo mining scheme, which made pool mining more and more popular [4,5,7]. In pool mining, all the miners in the pool will aggregate their computational power together to mine the new block, leading to an increased winning probability for the mining pool. When a miner in the pool reports a new valid block, the pool operator broadcasts it to all the miners on the network, and receives a reward of one block from the network. After that, the pool will distribute the rewards to its miners according to the predefined reward mechanism.
Up till now, many reward mechanisms have been proposed based on the PoW consensus protocol, such as the proportional mechanism, pay-per-share (PPS), Slushes method, Geometric method and pay-per-last-N-shares (PPLNS) [15]. Among the above mechanisms, PPLNS mechanism is regarded as one of the most widely used mechanisms adopted by pool operators, which distributes the reward according to the last N shares reported by the miners [15,26].
For all mechanisms including PPLNS, incentive compatibility is a very important characteristic for the miners to behave truthfully in the mining pools. However, the PPLNS mechanism has been proved to be incentive incompatible since it does not satisfy the condition for judgment of the incentive compatibility of a reward proposed by Schrijvers et al. [16]. As such, miners can increase their rewards through strategic behaviors such as delaying the reporting time of their found shares [26].
As can be seen in the PPLNS mechanism, only the last N shares are considered by the pool when it distributes the rewards among its miners. As such, the reporting order of the shares are of great importance, and if the shares reported by the miner are not in the last N shares, the miner can not get any reward from the pool. We call such issue as share reporting decision, and it has become an important problem faced by miners when they participate in mining with the PPLNS mechanism [12]. However, in the literature, the share reporting problem has not yet received sufficient attention from researchers.
This paper aims to study the share reporting issue faced by the miners in PPLNS pools, and as far as we know, this work is the first attempt to study this issue. Based on the expected value of random variable [2,23], we establish a share reporting optimization model for the miners to maximize the expected reward of the miners, and propose a hybrid share reporting strategy for the miners based on the established model. We also design several experiments utilizing the computational experiment approach [11,13,19,28], to validate the effectiveness of the proposed new share reporting strategy, and the results show that our proposed share reporting strategy outperforms two baseline strategies.
The organization of the rest of this paper is as follows. Section 2 describes the process of blockchain mining and the PPLNS reward mechanism. In Section 3, we study the expected reward in two commonly used share reporting strategies. In Section 4, we introduce the research issue, and propose a share reporting optimization model. In Section 5, we evaluate our proposed share reporting strategy with computational experiment approach. In Section 6, we draw conclusions of our paper.
Section snippets
Pool mining
The notations used in this paper are listed in Table 1.
In a mining pool, miners cooperate with each other to solve a challenging cryptographic puzzle by contributing their hashing power to the pool. In each round of blockchain mining, a new block can be found. When the new block is confirmed, the pool can win the block reward from the blockchain system, as well as the associated transaction fees from the users [14].
The detailed blockchain mining process is shown in Fig. 1, and can be described
Expected rewards in commonly used strategies
In pool mining, when formulating the share reporting strategies, the miner can not observe the reporting strategies of other miners. Thus, for each reporting strategy, there are multiple cases for the positions of the miner's shares, and the rewards of the miner under different cases may also differ. As such, we aim to optimize the miner's share reporting strategy, and propose a novel reporting strategy to maximize the expected rewards of the miner. In the following, we compute the expected
Expected reward based model
In this section, we establish the following expectation model to optimize the miner's reporting decisions under different values of N
In the following, we find the optimal strategies of model (29) under different N. We first compare the expected revenues in the two strategies, which can be given in the following theorem.
Theorem 3 For any W and 2 ≤ n < W, when , we have , when or j = W, we have , and when , we have
Computational experiments
In this section, we will validate the effectiveness of our proposed hybrid strategy for the miner in PPLNS pools with the computational experiments approach [24]. For comparison purpose, we adopt Packaging Strategy and Random Strategy as two baseline strategies.
Conclusions and future work
In this work, we mainly studied the share reporting issues faced by the miners in mining pools adopted the PPLNS reward mechanism. Considering that the share reporting strategy can greatly affect the rewards of the miners, we established a share reporting optimization model for the miners in PPLNS mining pools, which can help the miners find their optimal share reporting strategies under different values of N. Based on the established model, we propose a hybrid share reporting strategy. We also
Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (71702182, 71472174, 61533019, 71232006).
Rui Qin received her B.S., M.S. degrees in mathematics and applied mathematics, operational research and cybernetics from Hebei University, in 2007 and 2010, respectively, and received her Ph.D. degree in computer application technology from the University of Chinese Academy of Sciences, in 2016. She is currently an Assistant Professor with the State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China. She is also
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Rui Qin received her B.S., M.S. degrees in mathematics and applied mathematics, operational research and cybernetics from Hebei University, in 2007 and 2010, respectively, and received her Ph.D. degree in computer application technology from the University of Chinese Academy of Sciences, in 2016. She is currently an Assistant Professor with the State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China. She is also with the Qingdao Academy of Intelligent Industries, Qingdao, China.
Dr. Qin's research interests include blockchain, social computing, computational advertising and parallel management. Currently, Dr. Qin is the Associate Director of the CAA (Chinese Association of Automation) Technical Committee of Blockchain.
Yong Yuan received his B.S., M.S., and Ph.D. degrees in computer software and theory from the Shandong University of Science and Technology, Shandong, China, in 2001, 2004, and 2008, respectively. He is an Associate Professor at the State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China, and he is the Vice President of the Qingdao Academy of Intelligent Industries, Qingdao, China.
Dr. Yuan's research interests include blockchain, cryptocurrency and smart contract. He has authored over 90 papers published in academic journals and conferences. Currently, Dr. Yuan is the Associate Editor of IEEE Transactions on Computational Social Systems, and also Associate Editor of ACTA Automatica Sinica. He is a Senior Member of IEEE, and the Chair of IEEE Council on RFID Technical Committee on Blockchain, Co-chair of IEEE SMC Technical Committee on Blockchain, and also Director of the CAA (Chinese Association of Automation) Technical Committee of Blockchain. Dr. Yuan is the Secretary-general of IEEE SMC Technical Committee on Social Computing and Social Intelligence, Vice Chair of IFAC Technical Committee on Economic, Business and Financial Systems (TC 9.1), Chair of ACM Beijing Chapter on Social and Economic Computing. Dr. Yuan is also the Secretary-general of CAAI (Chinese Association of Artificial Intelligence) Technical Committee on Social Computing and Social Intelligence, Vice Director and Secretary-general of CAM (Chinese Academy of Management) Technical Committee on Parallel Management.
Fei-Yue Wang received the Ph.D. degree in computer and systems engineering from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1990. He joined the University of Arizona, Tucson, AZ, USA, in 1990, and became a Professor and the Director of the Robotics and Automation Laboratory and the Program in Advanced Research for Complex Systems. In 1999, he founded the Intelligent Control and Systems Engineering Center, Institute of Automation, Chinese Academy of Sciences (CAS), Beijing, China, under the support of the Outstanding Overseas Chinese Talents Program from the State Planning Council and “100 Talent Program” from CAS. In 2002, he joined the Lab of Complex Systems and Intelligence Science, CAS, as the Director, where he was the Vice President for Research, Education, and Academic Exchanges with the Institute of Automation from 2006 to 2010. In 2011, he was named as the State Specially Appointed Expert and Director of the State Key Laboratory for Management and Control of Complex Systems, Beijing, China. His current research interests include methods and applications for parallel systems, social computing, parallel intelligence, and knowledge automation.
Dr. Wang has been the general or program chair of more than 30 IEEE, INFORMS, ACM, and ASME conferences. He was the President of the IEEE ITS Society during 2005–2007, the Chinese Association for Science and Technology, USA, in 2005, and the American Zhu Kezhen Education Foundation during 2007–2008. He was the Vice President of the ACM China Council during 2010–2011, and chair of IFAC TC on Economic and Social Systems from 2008–2011. Currently, he is the President-Elect of IEEE Council on RFID. Since 2008, he has been the Vice President and the Secretary General of the Chinese Association of Automation. He was the Founding Editor-in-Chief of the International Journal of Intelligent Control and Systems during 1995–2000 and the IEEE ITS Magazine during 2006–2007. He was the EiC of the IEEE Intelligent Systems during 2009–2012 and the IEEE Transactions on ITS during 2009–2016. He is currently the EiC of the IEEE Transactions on Computational Social Systems, and the Founding EiC of the IEEE/CAA Journal of Automatica Sinica and the Chinese Journal of Command and Control. He was elected as a fellow of INCOSE, IFAC, ASME, and AAAS. In 2007, he was a recipient of the National Prize in Natural Sciences of China and was awarded the Outstanding Scientist by ACM for his research contributions in intelligent control and social computing. He was a recipient of the IEEE Intelligent Transporation Systems (ITS) Outstanding Application and Research Awards in 2009, 2011, and 2015, and the IEEE SMC Norbert Wiener Award in 2014.