Equilibria in the Nineteenth-Century Balance-of-Power System

This study examines a stochastic alliance equilibrium within the nineteenth-century balance-of-power system. Mathematical expressions for an alliance equilibrium are put forward and transition probabilities for the estimation of changes in the state of the system are derived. The Poisson expression for alliance formation also is derived as a consequence of the central equilibrium assumption. The nineteenth-century system is found to be heterogeneous in regard to both its component alliances and country participants. The importance of small powers in maintaining the structure of the balance-of-power system is emphasized.