Multi-team conflict resolution is ineffective for stable decision making

Competitive interactions between distinct groups or "teams" are ubiquitous across complex systems, from gene regulatory networks controlling cell fate decisions to political coalitions, economic markets, and social networks. While binary competition (two-team systems) dominates in biological contexts, multi-team competition is more common in social and economic domains, raising fundamental questions about the stability and reliability of different competitive architectures. Here, we systematically analyze the dynamics of multi-team competitive networks using Boolean modeling of signed directed graphs, extending well-characterized two-team gene regulatory networks to systems with three or more mutually inhibitory teams. Our results demonstrate that three-team networks produce significantly less stable outcomes than two-team systems, with steady states exhibiting higher "frustration" (structural imbalance) and increased sensitivity to perturbations. Multi-team systems show unpredictable state transitions even under controlled perturbations, particularly at lower network densities typical of real-world systems. Networks with four or more teams cannot maintain entirely distinct stable states. Using spectral analysis of the network adjacency matrices, we show that team structure can be predicted from eigenvector properties, extending structural balance theory to signed directed networks. These findings have broad implications across domains: in biology, they explain the evolutionary preference for binary cell-fate decisions and suggest why multi-fate systems are rare and unreliable. In social and political contexts, they provide insight into coalition instability and the tendency toward two-party systems. In economic networks, they illuminate the challenges of maintaining stable multi-competitor markets. Our work establishes fundamental principles governing the stability-complexity tradeoff in competitive network systems, with applications spanning systems biology, social network analysis, political science, and organizational theory.