Hierarchy of Membership and Burden Sharing in a Military Alliance

ABSTRACT

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.

KEYWORDS:

• Alliances
• public goods
• burden sharing
• free riding
• multi-tier Penrose-Stackelberg equilibrium
• NATO

JEL CLASSIFICATION:

• C72
• D62
• D74
• H41

Acknowledgments

Financial support from LISOMO at NES is gratefully acknowledged. Richard Eichenberg kindly provided insight on the public opinion data. We are grateful to Laura Gold for her help with the preparation of this manuscript.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

1. For more on the role of the Soviet Union within the Warsaw Pact, see Mastny and Byrne (2005).

2. For the distinctions between the 1989 end of the Cold War and the 1991 end of the Soviet Union, see Y. Weber (2016).

3. The Slovak Republic was part of the original Visegrad Group, but its accession was delayed by NATO until 2004 due to actions of its then-Prime Minister Vladimir Meciar being considered undemocratic by the organization.

4. Cornes and Sandler (1984b), which assumes a non-Nash behavior by alliance members, is an exception.

5. We are grateful to the referee for raising this point.

6. ³For applications of Penrose’s Square-Root Law see Kirsch (2013).

7. ⁴The idea of differentiating the countries according to their marginal rate of substitution has already been applied by Olson and Zeckhauser (1966) and Weber and Wiesmeth (1991a). However, in contrast to their model, countries in our approach are characterized by additional parameters. Moreover, our utility functions differ from those in S. Weber and Wiesmeth (1991a).