Mean Field Games of Capital Accumulation and Militarization among Nations

This paper develops a dynamic mean field game model of global arms races and capital accumulation among heterogeneous nations. Each country allocates its output among consumption, capital investment, and military spending, optimizing against an evolving global militarization level. Strategic interdependence is modeled through forward–backward stochastic differential equations, combining individual HJB equations, Population-level Fokker–Planck dynamics, and a mean field consistency condition. Closed-form solutions are derived under a linear–quadratic benchmark, and steady-state distributions are simulated for major powers including the U.S., China, Russia, and the EU. Results reveal how cross-country differences in productivity, military efficiency, and volatility lead to divergent long-run equilibria and global militarization traps. The model captures strategic path dependence and hysteresis, showing how shocks or preemptive arming can entrench high-arms outcomes. Policy implications include the importance of disarmament mechanisms, transparency, and coordinated institutions to escape inefficient militarized equilibria. The framework offers a robust tool for analyzing geopolitical dynamics under uncertainty.