Blockchain networks have attracted tremendous attention for creating cryptocurrencies and decentralized economies built on peer-to-peer protocols. However, the complex nature of the dynamics and feedback mechanisms within these economic networks has rendered it difficult to reason about the growth and evolution of these networks. Hence, proper mathematical frameworks to model and analyze the behavior of blockchain-enabled networks are essential. To address this need, we establish a formal mathematical framework, based on dynamical systems, to model the core concepts in blockchain-enabled economies. Drawing on concepts from differential games, control engineering, and stochastic dynamical systems, this paper proposes a methodology to model, simulate, and engineer networked token economies. To illustrate our framework, a model of a generalized token economy is developed, where miners provide a commodity service to a platform in exchange for a cryptocurrency and users consume a service from the platform. We illustrate the dynamics of token economies by simulating and testing two different block reward strategies. We then conclude by outlining future research directions that will integrate additional methods from signal processing and control theory into the toolkit for designers of blockchain-enabled economic systems.

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关于将基于区块链的经济网络建模为随机动力系统

区块链网络在创建基于对等协议的加密货币和去中心化经济方面引起了极大的关注。但是，这些经济网络中动态和反馈机制的复杂性使得很难对这些网络的增长和演化进行推理。因此，用于建模和分析基于区块链的网络行为的正确数学框架至关重要。为了满足这一需求，我们基于动力系统建立了一个正式的数学框架，以对基于区块链的经济体中的核心概念进行建模。借鉴差分博弈，控制工程和随机动力学系统的概念，本文提出了一种对网络代币经济进行建模，仿真和工程设计的方法。为了说明我们的框架，开发了一种通用代币经济模型，其中矿工向平台提供商品服务以换取加密货币，而用户则从平台消费服务。我们通过模拟和测试两种不同的区块奖励策略来说明代币经济的动态。然后，我们概述了未来的研究方向，这些研究方向将把信号处理和控制理论中的其他方法集成到面向区块链的经济系统设计人员的工具包中。