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Evolutionary Equilibrium Analysis for Decision on Block Size in Blockchain Systems

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))


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 time-varying transaction fees. The transaction fees are offered by the senders whose transactions are packaged into blocks and is positively correlated with the block size. However, the larger size of a block brings the longer latency, resulting in a smaller probability of successfully mining. Therefore, finding the optimal block size to trade off these two factors is a complex and crucial problem for the mining pools. In this paper, we model a repeated mining competition dynamics in blockchain system as an evolutionary game to study the interactions among mining pools. In this game, each pool has two strategies: to follow the default size \(\bar{B}\), i.e., the upper bound of a block size, or not follow. Because of the bounded rationality, each mining pool pursues its evolutionary stable block size (ESS) according to the mining pools’ computing power and other factors by continuous learning and adjustments during the whole mining process. A study framework is built for the general evolutionary game, based on which we then theoretically explore the existence and stability of the ESSs for a case of two mining pools. Numerical experiments with real Bitcoin data are conducted to show the evolutionary decisions of mining pools and to demonstrate the theoretical findings in this paper.

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  1. Chen, J., Cheng, Y., Xu, Z., Cao, Y.: Evolutionary equilibrium analysis for decision on block size in blockchain systems (full version) (2021).

  2. Easley, D., OHara, M., Basu, S.: From mining to markets: the evolution of bitcoin transaction fees. J. Financ. Econ. 134, 91–109 (2019)

    Google Scholar 

  3. Friedman, D.: On economic applications of evolutionary game theory. J. Evol. Econ. 8(1), 15–43 (1998)

    Article  Google Scholar 

  4. Garay, J., Kiayias, A., Leonardos, N.: The bitcoin backbone protocol: analysis and applications. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 281–310. Springer, Heidelberg (2015).

    Chapter  Google Scholar 

  5. Gervais, A., Karame, G.O., Wüst, K., Glykantzis, V., Ritzdorf, H., Capkun, S.: On the security and performance of proof of work blockchains. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, CCS 2016, p. 3C16. Association for Computing Machinery (2016)

    Google Scholar 

  6. Houy, N.: The bitcoin mining game. Lcloud/fogr J. 1(13), 53–68 (2016)

    Google Scholar 

  7. Jiang, S., Wu, J.: Bitcoin mining with transaction fees: a game on the block size. In: 2019 IEEE International Conference on Blockchain (Blockchain), pp. 107–115 (2019)

    Google Scholar 

  8. Li, J., Kendall, G., John, R.: Computing nash equilibria and evolutionarily stable states of evolutionary games. IEEE Trans. Evol. Comput. 20(3), 460C469 (2016)

    Google Scholar 

  9. Liu, X., Wang, W., Niyato, D., Zhao, N., Wang, P.: Evolutionary game for mining pool selection in blockchain networks. IEEE Wirel. Commun. Lett. 7(5), 760–763 (2018)

    Article  Google Scholar 

  10. Lombrozo, E., Lau, J., Wuille, P.: Segregated witness (consensus layer) (2015).

  11. Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system (2008).

  12. NervosFans: Bitcoin transaction fee rules.

  13. Pan, D., Zhao, J.L., Fan, S., Zhang, Z.: Dividend or no dividend in delegated blockchain governance: a game theoretic analysis. J. Syst. Sci. Syst. Eng. 30, 1861–9576 (2021)

    Article  Google Scholar 

  14. Rizun, P.R.: A transaction fee market exists without a block size limit, block Size Limit Debate Working Paper (2015)

    Google Scholar 

  15. TOKENVIEW: Bitcoin browser.

  16. Zhang, R., Preneel, B.: On the necessity of a prescribed block validity consensus: analyzing bitcoin unlimited mining protocol. In: Proceedings of the 13th International Conference on Emerging Networking Experiments and Technologies, p. 108C119. Association for Computing Machinery, New York (2017)

    Google Scholar 

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This work is partially supported by the National Nature Science Foundation of China (No. 11871366), Qing Lan Project of Jiangsu Province, the Research Innovation Program for College Graduate Students of Jiangsu Province (No. KYCX21-2998 and KYCX20-2790), and the project of the philosophy & social sciences of higher education in Jiangsu province. (No. 2018SJA1347).

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Correspondence to Yukun Cheng .

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Chen, J., Cheng, Y., Xu, Z., Cao, Y. (2021). Evolutionary Equilibrium Analysis for Decision on Block Size in Blockchain Systems. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

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