Power Allocation Games on Signed Networks: Nash Equilibria and Coevolutionary Dynamics

Abstract

Understanding how strategic interactions and power distributions coevolve in international relations is central to explaining conflict, cooperation, and long-term inequality. We study this problem using a power-allocation game on signed networks. Departing from models that restrict strategy updates to Pareto improvements, we propose a generalized formulation in which countries prioritize self-survival and strategically trade off between supporting allies and weakening adversaries. This relaxation allows countries to sacrifice certain allies to achieve higher overall payoffs. For the resulting static game, we establish the existence of pure-strategy Nash equilibria and characterize their properties in extreme cases, including fully antagonistic networks and the presence of a dominant power. We further introduce a power-strategy coevolutionary dynamic and prove its almost-sure convergence to equilibria corresponding to the static game. The proposed models are validated using empirical data and numerical simulations. Historical data from the Correlates of War and national capability datasets show that survival likelihood predicts countries' safety outcomes and subsequent economic growth with relatively high accuracy. Simulations further indicate that, under fixed conflict intensity, more structurally balanced signed networks yield higher average power and lower inequality at steady states.