Evolutionary Game for Mining Pool Selection in Blockchain Networks

arXiv:1712.02027

Date: 2017-12-29

Author(s): Xiaojun Liu, Wenbo Wang, Dusit Niyato, Narisa Zhao, Ping Wang

Link to Paper

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Abstract

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 about the blockchain state. The block miners have to devote their computation power measured in hash rate in a crypto-puzzle solving competition to win the reward of publishing (a.k.a., mining) new blocks. Due to the exponentially increasing difficulty of the crypto-puzzle, individual block miners tends to join mining pools, i.e., the coalitions of miners, in order to reduce the income variance and earn stable profits. In this paper, we study the dynamics of mining pool selection in a blockchain network, where mining pools may choose arbitrary block mining strategies. We identify the hash rate and the block propagation delay as two major factors determining the outcomes of mining competition, and then model the strategy evolution of the individual miners as an evolutionary game. We provide the theoretical analysis of the evolutionary stability for the pool selection dynamics in a case study of two mining pools. The numerical simulations provide the evidence to support our theoretical discoveries as well as demonstrating the stability in the evolution of miners' strategies in a general case.

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References

[1] S. Nakamoto, “Bitcoin: A peer-to-peer electronic cash system,” Selfpublished Paper, May 2008.

[2] F. Tschorsch and B. Scheuermann, “Bitcoin and beyond: A technical survey on decentralized digital currencies,” IEEE Communications Surveys Tutorials, vol. 18, no. 3, pp. 2084–2123, third quarter 2016.

[3] J. Garay, A. Kiayias, and N. Leonardos, “The bitcoin backbone protocol: Analysis and applications,” in 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, Apr. 2015, pp. 281–310.

[4] P. R. Rizun, “A transaction fee market exists without a block size limit,” Self-published Paper, Aug. 2015.

[5] N. Houy, “The bitcoin mining game,” Ledger Journal, vol. 1, no. 13, pp. 53 – 68, 2016.

[6] B. A. Fisch, R. Pass, and A. Shelat, “Socially optimal mining pools,” arXiv preprint arXiv:1703.03846, 2017.

[7] J. Hofbauer and K. Sigmund, “Evolutionary game dynamics,” Bulletin of the American Mathematical Society, vol. 40, no. 4, pp. 479–519, 2003.

[8] J. Hofbauer and W. H. Sandholm, “Stable games and their dynamics,” Journal of Economic Theory, vol. 144, no. 4, pp. 1665 – 1693.e4, 2009.

[9] J. W. Weibull, Evolutionary game theory. MIT press, 1997.