A Game-Theoretic Model of Global AI Development Race: Dynamics of Domination and Technological Catch-up

This paper presents a novel game-theoretic model simulating the global artificial intelligence (AI) development race among nations. We introduce a dynamic system of equations that captures the complex interplay between a country's development level, investment strategies, market share, and the possibility of technological domination. The model incorporates key features of technological races, including returns subject to diminishing marginal utility, exponentially increasing costs, market dynamics, and strategic investment decisions based on relative market positions. Through Monte Carlo simulations, we analyze various scenarios of the AI race, focusing on the emergence of dominant players and the challenges faced by countries attempting to catch up. Our results indicate a tendency towards oligopolistic market structures, with a few countries achieving technological domination while others struggle to close the gap. The model provides insights into the potential trajectories of global AI development and the conditions under which technological leapfrogging might occur. These findings have implications for policymakers and researchers in understanding the dynamics of technological races and formulating strategies for national AI development.