Hierarchy of Membership and Burden Sharing in a Military Alliance

We examine a military alliance with heterogeneous members that finances the production of the 'alliance good' (defense, deterrence, and peacekeeping) through its members' voluntary contributions. To examine the patterns of those contributions, we introduce a decision-making model with three layers of hierarchy: one 'super-leader', a group of 'leaders', and several 'followers', which takes into account different economic and historical backgrounds of member states. The asymmetric interaction between the members is reflected by the choice of Stackelberg paradigm where the sequence of countries' moves is determined by their alliance status. We then apply Penrose's Law to incorporate countries' heterogeneous population sizes in our model and show the existence of a unique Penrose-Stackelberg equilibrium. We apply our results to NATO and offer an empirical evaluation of burden sharing across the alliance by showing how economic characteristics, alliance 'awareness', and the alliance status explain the patterns of members' contributions. We also evaluate the optimal fit between the data and an appropriate choice of the alliance's hierarchical structure.