We present a novel framework for analyzing blockchain consensus mechanisms by modeling blockchain growth as a Partially Observable Stochastic Game (POSG) which we reduce to a set of Partially Observable Markov Decision Processes (POMDPs) through the use of the mean field approximation. This approach formalizes the decision-making process of miners in Proof-of-Work (PoW) systems and enables a principled examination of block selection strategies as well as steady state analysis of the induced Markov chain. By leveraging a mean field game formulation, we efficiently characterize the information asymmetries that arise in asynchronous blockchain networks. Our first main result is an exact characterization of the tradeoff between network delay and PoW efficiency--the fraction of blocks which end up in the longest chain. We demonstrate that the tradeoff observed in our model at steady state aligns closely with theoretical findings, validating our use of the mean field approximation. Our second main result is a rigorous equilibrium analysis of the Longest Chain Rule (LCR). We show that the LCR is a mean field equilibrium and that it is uniquely optimal in maximizing PoW efficiency under certain mild assumptions. This result provides the first formal justification for continued use of the LCR in decentralized consensus protocols, offering both theoretical validation and practical insights. Beyond these core results, our framework supports flexible experimentation with alternative block selection strategies, system dynamics, and reward structures. It offers a systematic and scalable substitute for expensive test-net deployments or ad hoc analysis. While our primary focus is on Nakamoto-style blockchains, the model is general enough to accommodate other architectures through modifications to the underlying MDP.

翻译：我们提出了一种分析区块链共识机制的新框架，通过将区块链增长建模为部分可观测随机博弈（POSG），并利用平均场近似将其简化为一系列部分可观测马尔可夫决策过程（POMDP）。该方法形式化了工作量证明（PoW）系统中矿工的决策过程，支持对区块选择策略进行原理性检验，并对所诱导的马尔可夫链进行稳态分析。通过采用平均场博弈公式，我们有效刻画了异步区块链网络中产生的信息不对称性。我们的第一个主要成果是精确描述了网络延迟与PoW效率（最终进入最长链的区块比例）之间的权衡关系。我们证明，模型中观察到的稳态权衡与理论发现高度吻合，从而验证了平均场近似的适用性。第二个主要成果是对最长链规则（LCR）进行了严格的均衡分析。我们证明LCR是一种平均场均衡，且在特定温和假设下是最大化PoW效率的唯一最优策略。该结果为去中心化共识协议中持续采用LCR提供了首个形式化依据，兼具理论验证与实践启示。除核心成果外，本框架支持灵活试验替代性区块选择策略、系统动态与奖励结构，为昂贵的测试网部署或临时性分析提供了系统化、可扩展的替代方案。虽然主要关注中本聪式区块链，但该模型具有足够通用性，可通过修改底层MDP适配其他体系结构。