This paper presents a novel solution concept, called BAR Nash Equilibrium (BARNE) and apply it to analyse the Verifier's dilemma, a fundamental problem in blockchain. Our solution concept adapts the Nash equilibrium (NE) to accommodate interactions among Byzantine, altruistic and rational agents, which became known as the BAR setting in the literature. We prove the existence of BARNE in a large class of games and introduce two natural refinements, global and local stability. Using this equilibrium and its refinement, we analyse the free-rider problem in the context of byzantine consensus. We demonstrate that by incorporating fines and forced errors into a standard quorum-based blockchain protocol, we can effectively reestablish honest behavior as a globally stable BARNE.

翻译：本文提出了一种新的解概念——BAR纳什均衡（BARNE），并将其应用于分析区块链中的基础问题——验证者困境。我们的解概念对纳什均衡（NE）进行了扩展，以容纳拜占庭、利他和理性智能体之间的交互，这在文献中被称为BAR设定。我们证明了一类广泛博弈中BARNE的存在性，并引入两种自然的精炼形式——全局稳定性和局部稳定性。利用该均衡及其精炼形式，我们分析了拜占庭共识背景下的搭便车问题。通过将罚款和强制错误引入基于法定人数的标准区块链协议中，我们证明能够有效地将诚实行为重建为全局稳定的BARNE。