Engineers building distributed multi-agent systems routinely overestimate how well their systems will scale. This paper surveys the mathematical results that explain why and what to do about it. We examine three classes of hard limits: (1) communication complexity forcing quadratic message growth, (2) consensus algorithm instabilities that emerge at scale, and (3) network effect phase transitions that cause unpredictable failures. Flat coordination hits practical limits around 100 agents. We then examine what works: hierarchical architectures, adaptive algorithms, weak coupling, and monitoring for phase transitions. We synthesize results from distributed computing, control theory, and statistical physics to provide both a realistic picture of scaling limits and practical guidance for building systems that work at scale.
Engineers building distributed multi-agent systems routinely overestimate how well their systems will scale. This paper surveys the mathematical results that explain why and what to do about it. We examine three classes of hard limits: (1) communication complexity forcing quadratic message growth, (2) consensus algorithm instabilities that emerge at scale, and (3) network effect phase transitions that cause unpredictable failures. Flat coordination hits practical limits around 100 agents. We then examine what works: hierarchical architectures, adaptive algorithms, weak coupling, and monitoring for phase transitions. We synthesize results from distributed computing, control theory, and statistical physics to provide both a realistic picture of scaling limits and practical guidance for building systems that work at scale.