Abstract. This paper is devoted to global power hierarchies. A global power hierarchy is a three-level control system, with the upper level occupied by a Principal. The second (middle) level consists of influence agents subordinate to the Principal. At the third (lower) level, there are basic agents subordinate to influence agents. The model is considered in a dynamic discrete-time setting. An algorithm is formulated to solve the Germeier game Г1t. The model is studied via computer simulations using both model input parameters and data corresponding to global realities for the period fr om 1990 to 2025. The simulation results are analyzed. In particular, conditions for the emergence of a unipolar, bipolar, and multipolar power hierarchy at the global level are established. As shown, the main condition for a multipolar world is a large initial quantity of resources. If this quantity is sufficiently large, then regardless of the values of competition parameters, the world becomes multipolar. In practice, however, all resources are lim ited; therefore, a bipolar or unipolar world emerges, depending on the strength of power hierarchies and the values of competition parameters.
Keywords: power hierarchies, simulation modeling, Germeier games, Nash equilibrium, difference games.
Acknowledgments. This work was supported by the Russian Science Foundation, project no. 25-11-00094.
Ougolnitsky, G.A. and Usov, A.B., Models of Power Hierarchies at the Global Level. Control Sciences 3, 34–41 (2026).
Models of Power Hierarchies at the Global Level