Recent work in the field of multi-agent systems has sought to use techniques and concepts from the field of formal methods to provide rigorous theoretical analysis and guarantees on complex systems where multiple agents strategically interact, leading to the creation of the field of equilibrium analysis, which studies equilibria concepts from the field of game theory through a complexity-theoretic lens. Multi-agent systems, however, are complex mathematical objects, and, therefore, defining them in a precise mathematical manner is non-trivial. As a result, researchers often considered more restrictive models that are easier to model but lack expressive power or simply omit critical complexity-theoretic results in their analysis. This paper addresses this problem by carefully analyzing and contrasting complexity-theoretic results in the explicit model, a mathematically precise formulation of the models commonly used in the literature, and the circuit-based model, a novel model that addresses the problems found in the literature. The utility of the circuit-based model is demonstrated through a comprehensive analysis that considers upper and lower bounds for the realizability and verification problems, the two most important decision problems in equilibrium analysis, for both models. By conducting this analysis, we see that problematic issues that are endemic to the explicit model and the equilibrium analysis literature as a whole are adequately handled by the circuit-based model.

翻译：近年来，多智能体系统领域的研究致力于采用形式化方法领域的技术与概念，对多个智能体进行策略性交互的复杂系统提供严格的理论分析与性能保证，由此催生了均衡分析这一子领域。该领域通过复杂性理论的视角研究博弈论中的均衡概念。然而，多智能体系统作为复杂的数学对象，其精确数学定义并非易事。因此，研究者往往采用限制性更强、易于建模但表达能力较弱的模型，或在分析中直接省略关键的复杂性理论结果。本文通过系统对比显式模型（文献中常用模型的精确数学形式化表述）与电路模型（旨在解决现有文献缺陷的新型模型）的复杂性理论结果来解决上述问题。通过综合考虑两种模型中均衡分析最重要的两个决策问题——可实现性与可验证性——的上下界，我们完成了对电路模型效用的全面论证分析。研究表明，显式模型及整个均衡分析文献中普遍存在的典型问题，在电路模型中均能得到妥善处理。