Simulating Why One AI Always Wins: Formal Theory of the Singleton Attractor (github.com)

A new formal model developed at the University of North Carolina at Greensboro combines three established frameworks in AI dynamics to examine the emergence of a dominant AI agent, termed a "singleton." This model integrates Yudkowsky's intelligence explosion, Omohundro's resource acquisition principles, and Lotka-Volterra competitive exclusion theory into a coupled ordinary differential equation (ODE) system. It establishes conditions under which a single AI could outcompete its peers and includes empirical testing against various AI capability metrics through 2026. The findings highlight that if certain conditions—specifically a key assumption about strategy dynamics—hold true, a singular dominant agent can emerge in a finite time frame, raising crucial implications for the future landscape of AI development. The research is particularly significant for the AI/ML community as it presents a mathematical framework that could help predict and understand shifts in competitive dynamics as AI capabilities evolve. The paper details several theorems about capability divergence and coalition strategies while empirically challenging the assumption of inevitable singleton emergence. Notably, preliminary data suggests that the critical condition for a singleton's rise has not been supported through the tested proxies. This work not only advances theoretical discussions around AI dominance but also emphasizes the need for ongoing scrutiny of underlying assumptions regarding AI scalability and competition, guiding future policy and research efforts in the rapidly evolving field.