In this paper, we analyze the behavior of a multi-agent system driven by the interactions of agents within a competitive environment. To achieve this, we describe the transition probabilities that underlie the system's stochastic nature. We also derive the Fokker-Planck equations for the density distribution of the number of agents in the system and solve these equations for specific cases.

翻译：本文分析了一个由竞争环境中智能体间交互驱动的多智能体系统的行为。为此，我们描述了构成系统随机性基础的转移概率。同时，我们推导了系统内智能体数量密度分布的福克-普朗克方程，并针对特定情况求解了这些方程。