A Novel Two-Stage Game Model for Pricing Cloud/ Fog Computing Resource in Blockchain Systems

Jinmian Chen, Yukun Cheng, Zhiqi Xu
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Abstract

Cloud/fog computing resource pricing is a new paradigm in the blockchain mining scheme, as the participants would like to purchase the cloud/fog computing resource to speed up their mining processes. In this paper, we propose a novel two-stage game to study the optimal price-based cloud/fog computing resource management, in which the cloud/fog computing resource provider (CFP) is the leader, setting the resource price in Stage I, and the mining pools act as the followers to decide their demands of the resource in Stage II. Since mining pools are bounded rational in practice, we model the dynamic interactions among them by an evolutionary game in Stage II, in which each pool pursues its evolutionary stable demand based on the observed price, through continuous learning and adjustments. Backward induction method is applied to analyze the sub-game equilibrium in each stage. Specifically in Stage II, we first build a general study framework for the evolutionary game model, and then provide a detailed theoretical analysis for a two-pool case to characterize the conditions for the existence of different evolutionary stable solutions. Referring to the real world, we conduct a series of numerical experiments, whose results validate our theoretical findings for the case of two mining pools. Additionally, the impacts from the size of mining block, the unit transaction fee and the price of token on the decision makings of participants are also discussed.
区块链系统中云/雾计算资源定价的新型两阶段博弈模型
云/雾计算资源定价是区块链挖矿方案中的一个新范式,因为参与者希望购买云/雾计算资源来加快他们的挖矿过程。本文提出了一种新的两阶段博弈方法来研究基于价格的云/雾计算资源最优管理,其中云/雾计算资源提供商(CFP)作为第一阶段的领导者来设定资源价格,矿池作为追随者来决定第二阶段对资源的需求。由于矿池在实践中是有限理性的,我们通过第二阶段的进化博弈来模拟矿池之间的动态交互,在第二阶段中,每个矿池通过不断的学习和调整,根据观察到的价格追求其进化稳定的需求。采用逆向归纳法对各阶段的子博弈均衡进行了分析。具体而言,在第二阶段,我们首先构建了进化博弈模型的一般研究框架,然后对两池情况进行了详细的理论分析,以表征不同进化稳定解存在的条件。参考现实世界,我们进行了一系列数值实验,其结果验证了我们在两个矿池情况下的理论发现。此外,还讨论了挖矿区块大小、单位交易费用和代币价格对参与者决策的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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