External security threats create incentives for international cooperation, but they
do not determine which countries cooperate or whether the resulting coalition is stable.
We develop a framework of supranational security cooperation in which countries dif
fer in the benefits they derive from collective protection and form expectations about
the participation of others. Building on the economics of alliance burden sharing and
a prospective model of coalition formation, we characterize stable partial coalitions
and show how changes in the external threat can alter the set of sustainable coalition
structures. Country-specific benefits depend jointly on population, economic size, and
geographic exposure, allowing a common security environment to generate heteroge
neous incentives to participate. We apply the framework to the European Sky Shield
Initiative (ESSI). The observed ESSI membership does not satisfy the model’s stability
conditions, whereas alternative configurations that include Italy, France, or both can
be stable over distinct ranges of the threat parameter. The analysis shifts the focus
from how members of an existing alliance share the burden of collective defense to
the prior question of which countries participate in the first place. More generally, it
shows how heterogeneous benefits and changing external threats jointly select among
alternative stable security coalitions.

README and Guidance
Overview
The replication package contains R code that constructs the analysis dataset
and performs all model computations. The model calculations are organized
into two primary directories, which generate the model results along with the
corresponding figures and tables presented in the paper. In addition, three
separate scripts are included to produce the treemaps, visualize data on the
world map, and compute the Wilcoxon test results. Altogether, the replication
package comprises 37 code files.
Data Availability and Provenance Statements
□ This paper does not involve analysis of external data (i.e., no data are used
or the only data are generated by the authors via simulation in their code).
If box above is checked and if no simulated/synthetic data files
are provided by the authors, please skip directly to the section on
Computational Requirements. Otherwise, continue.
The data used to calculate the Average Benefit Shares and to conduct the
Wilcoxon tests—including annual country-level GDP, population, and military
expenditures—were obtained from the World Bank (2024) via its API on Novem
ber 8, 2024. The following indicators were used:
• NY.GDP.MKTP.CD (GDP in current US$)
• MS.MIL.XPND.CD (Military expenditures in current US$)
• SP.POP.TOTL (Total population)
The data are publicly available at:
• https://data.worldbank.org/indicator/MS.MIL.XPND.CD
• https://data.worldbank.org/indicator/NY.GDP.MKTP.CD
• https://data.worldbank.org/indicator/SP.POP.TOTL
Data on the total length of borders between neighboring countries and Russia
were obtained from Statista (2024), based on information from the The World
Factbook provided by the Central Intelligence Agency (2022). The underlying
source can be accessed at:
• https://www.cia.gov/the-world-factbook
Data on exposed borders were obtained from the replication file of Sandler and
Shimizu (2014), which is based on data from the The World Factbook published
by the CIA (2011). The replication file was downloaded from:
• https://personal.utdallas.edu/ tms063000/website/downloads.html
1
However, the file is no longer available at this location (accessed February 17,
2026). Since the data originate from the CIA World Factbook (2011), they may
alternatively be retrieved directly from:
• https://www.cia.gov/the-world-factbook
Statement about Rights
□ I certify that the author(s) of the manuscript have legitimate access to and
permission to use the data used in this manuscript.
□ I certify that the author(s) of the manuscript have documented permission
to redistribute/publish the data contained within this replication package.
Appropriate permission are documented in the LICENSE.txt file.
Summary of Availability
□ All data are publicly available.
□ Some data cannot be made publicly available.
□ No data can be made publicly available.
□ Confidential data used in this paper and not provided as part of the public
replication package will be preserved for ___ years after publication, in
accordance with journal policies.
Details on each Data Source
Data.Name
Data.Files
Location
Provided
Citation
“GDP
(current
US$)”
“Population,
total”
“Military
expenditure
(current
USD)”
“Exposed
border to
Russia”
“Exposed
border”
wdi_indicators
08.11.2024.rds
wdi_indicators
08.11.2024.rds
wdi_indicators
08.11.2024.rds
statistic
id1306576
laenge-der
grenzen-von
russland-zu
benachbarten
staaten.xlsx
replication
data.dta
data/
ME/data/
data/
ME/data/
data/
ME/data/
data/
ME/data/
data/
TRUE
TRUE
TRUE
TRUE
TRUE
Worldbank
(2024)
Worldbank
(2024)
Worldbank
(2024)
CIA (2022)
CIA (2011)
2
Computational requirements
Software Requirements
□ The replication package contains one or more programs to install all
dependencies and set up the necessary directory structure. [HIGHLY
RECOMMENDED]
• RStudio (2025.9.2.418)
• R4.5.2– tidyverse (2.0.0)– WDI (2.7.9)– haven (2.5.5)– countrycode (1.6.1)– rlang (1.1.6)– dplyr (1.1.4)– conflicted (1.2.0)– rnaturalearth (1.1.0)– ggplot2 (4.0.1)
Controlled Randomness
□ Random seed is set at line _____ of program ______
■ No Pseudo random generator is used in the analysis described here.
Memory, Runtime, Storage Requirements
Summary Approximate time needed to reproduce the analyses on a standard
(2026) desktop machine:
□ <10 minutes
■ 10-60 minutes
□ 1-2 hours
□ 2-8 hours
□ 8-24 hours
□ 1-3 days
□ 3-14 days
□ > 14 days
Approximate storage space needed:
□ < 25 MBytes
□ 25 MB- 250 MB
□ 250 MB- 2 GB
■ 2 GB-25 GB
□ 25 GB- 250 GB
3
□ > 250 GB
□ Not feasible to run on a desktop machine, as described below.
Details The code was last run on a 8-core Intel-based laptop with Win
dows 11 with 700GB of free space.
Description of programs/code
INSTRUCTIONS: Give a high-level overview of the program files and
their purpose. Remove redundant/ obsolete files from the Replication
archive.
• The file ESSI-Map.R generates a figure of the worldmap included in the
paper displaying weather countries are part of the NATO, ESSI or Free
Riders.
• The file treemaps.R generates two treemaps showing the relative GDP
and military expenditures of European NATO members.
• The file Wilcoxon.R performs the Wilcoxon rank-sum tests comparing
European NATO members’average benefit shares with their defense burden,
proxied by each country’s military expenditures. The results are stored in
the data frame stat_data.
• Rfiles in ME/ generate all tables and figures in the main text related to the
model calculations that use GDP as a proxy for a country’s contribution
to the ESSI. Each script computes results for a specific combination of (i)
ESSI member set, (ii) benefit-sharing mechanism, and (iii) threat-factor
specification. The filename suffixes 15, 22, 22+Italy, 22+France, and
22+Italy
+France indicate the ESSI member set used. The suffixes ed and ud
denote equal and unequal weighting, respectively, when computing the
threat factor based on distance categories. Filenames without an additional
suffix, as well as those ending in ub, refer to threat-factor calculations based
on exposed border length to Russia, using equal and unequal weighting,
respectively. The computed results and model equilibria are printed to the
RStudio console during execution.
• Rfiles in GDP/ generate all tables and figures in the main text related to the
model calculations that use GDP as a proxy for a country’s contribution
to the ESSI. Each script computes results for a specific combination of
(i) ESSI member set, (ii) benefit-sharing mechanism, and (iii) threat
factor specification. The filename suffixes 22, 22+Italy, 22+France, and
22+Italy
+France indicate the ESSI member set used. The suffixes ed and ud
denote equal and unequal weighting, respectively, when computing the
threat factor based on distance categories. Filenames without an additional
suffix, as well as those ending in ub, refer to threat-factor calculations based
on exposed border length to Russia, using equal and unequal weighting,
4
respectively. The computed results and model equilibria are printed to the
RStudio console during execution.
Instructions to Replicators
• Install required R-Packages in R-Studio
• All necessary data files are included in the replication package. Executing
all scripts reproduces the figures presented in the paper. The model
equilibrium calculations are printed to the RStudio console during execution.
The Wilcoxon test results are stored in the data frame stat_data.
Details
• programs/00_setup.do: will create all output directories, install needed
ado packages.– If wishing to update the ado packages used by this archive, change
the parameter update_ado to yes. However, this is not needed to
successfully reproduce the manuscript tables.
• programs/01_dataprep:– These programs were last run at various times in 2018.– Order does not matter, all programs can be run in parallel, if needed.– A programs/01_dataprep/main.do will run them all in sequence,
which should take about 2 hours.
• programs/02_analysis/main.do.– If running programs individually, note that ORDER IS IMPORTANT.– The programs were last run top to bottom on July 4, 2019.
• programs/03_appendix/main-appendix.do. The programs were last run
top to bottom on July 4, 2019.
• Figure 1: The figure can be reproduced using the data provided in the folder
“2_data/data_map”, and ArcGIS Desktop (Version 10.7.1) by following
these (manual) instructions:– Create a new map document in ArcGIS ArcMap, browse to the
folder “2_data/data_map” in the “Catalog”, with files “provincebor
ders.shp”, “lakes.shp”, and “cities.shp”.– Drop the files listed above onto the new map, creating three separate
layers. Order them with “lakes” in the top layer and “cities” in the
bottom layer.– Right-click on the cities file, in properties choose the variable
“health”... (more details)
List of tables and programs
The provided code reproduces:
■ All numbers provided in text in the paper
■ All tables and figures in the paper
□ Selected tables and figures in the paper, as explained and justified below.
5
Figure/Table

Program
Output file
Note
Table 1
Figure 1
Table 2
Table 3
Table 4
Figure 2
Table 5
Table 6
Figure 3
Table 7
Table 8
Figure 4
Table 9
Figure 5
Table 10
Figure 6
Table 11
Figure 7
ME/Equilibria_
Be_Ge_NE.R
ESSI-Map.R
ME/Equilibria_
ESSI_15.R
ME/Equilibria_
ESSI_22.R
ME/Equilibria_
ESSI_22+Italy.R
ME/Equilibria_
ESSI_22+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
treemaps.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
Be_Ge_Ne.R
ME/Equilibria_
Be_Ge_Ne.R
Results are
printed in the
console
essi_map.pdf
treemap_me.pdf
treemap_gdp.pdf
utility_7.75.pdf
6
Results are
printed in the
console
Results are
printed in the
console
Results are
printed in the
console
Data is saved in
the data frame
data_fct
Results are saved
in the data frame
ex_nash
Data is saved in
the data frame
data_fct_1_2_3
Results are saved
in the data frame
ex_nash_grouped_1_2,
ex_nash_grouped_1_3,
ex_nash_grouped_1_2_3
Figure/Table

Program
Output file
Note
Table 12
Table 13
Table 14
Table 15
Table 16
Table 17
Table 18
Figure 8
Table 19
ME/Equilibria_
ESSI_22_ed.R
Wilcoxon.R
ME/Equilibria_
ESSI_22.R
GDP/Equilibria_
ESSI_15.R
GDP/Equilibria_
ESSI_22.R
GDP/Equilibria_
ESSI_22.R
GDP/Equilibria_
ESSI_22+Italy.R
GDP/Equilibria_
ESSI_22+France.R
GDP/Equilibria_
ESSI_22+Italy
+France.R
GDP/Equilibria_
ESSI_22+Italy
+France.R
GDP/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
Data is saved in
the data frame eu
rope_threat_weight
Results are saved
in the data frame
stat_data
Data is saved in
the data frame
data_fct
Results are
generated upon
adding or
removing the
respective
countries from the
data frame
participants_essi.
The corresponding
output is printed
in the console.
Results are
printed in the
console
Data is saved in
the data frame
data_fct
GDP/plt_share_
of_burden_bar_
europe.pdf
7
Results are saved
in the data frame
ex_nash after
filtering for
alpha_0 = 7.75
Figure/Table

Program
Output file
Note
Table 20
Table 21
Figure 9
ME/Equilibria_
ESSI_15.R
ME/Equilibria_
ESSI_22.R
ME/Equilibria_
ESSI_22.R
ME/Equilibria_
ESSI_22+Italy.R
ME/Equilibria_
ESSI_22+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
Figure 10 ME/Equilibria_
ESSI_22.R
Table 22
ME/Equilibria_
ESSI_22_ed.R
Figure 11 ME/Equilibria_
ESSI_22_ed.R
Figure 12 ME/Equilibria_
ESSI_22_ed.R
Results are
generated upon
adding or
removing the
respective
countries from the
data frame
participants_essi.
The corresponding
output is printed
in the console.
Results are
printed in the
console
ME/plt_share_
of_burden_bar_
europe.pdf
ME/plt_vip_
breakpoint.pdf
ME/plt_share_
of_burden_bar_
europe.pdf
ME/plt_vip_
breakpoint.pdf
8
Data is saved in
the data frame
data_fct
Figure/Table

Program
Output file
Note
Table 23
Table 24
Table 25
ME/Equilibria_
ESSI_22.R
ME/Equilibria_
ESSI_22+Italy.R
ME/Equilibria_
ESSI_22+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
ME/Equilibria_
ESSI_22+Italy
+France.R
Results are
generated when
Portugal and
Albania are added
and Poland and
the respective
countries are
removed from the
data frame
participants_essi.
The corresponding
output is printed
in the console
Results
corresponding to
the inclusion of
Portugal and
Albania and the
removal of Poland
from
participants_essi
are stored in the
data frame
ex_nash_grouped
after filtering for
alpha_0 = 6.385
Data
corresponding to
the inclusion of
Portugal and
Albania and the
removal of Poland
from
participants_essi
are stored in the
data frame
data_fct
9
Figure/Table

Program
Output file
Note
Figure 13 ME/Equilibria_
ESSI_22+Italy
+France.R
Table 26
Table 27
GDP/Equilibria_
ESSI_22.R
GDP/Equilibria_
ESSI_22+Italy.R
GDP/Equilibria_
ESSI_22+France.R
GDP/Equilibria_
ESSI_22+Italy
+France.R
GDP/Equilibria_
ESSI_22+Italy
+France.R
ME/utility_6.385_
24.pdf
10
The PDF is
generated when
Portugal and
Albania are
included and
Poland is removed
from
participants_essi.
Results are
generated when
Portugal and
Albania are added
and Poland and
the respective
countries are
removed from the
data frame
participants_essi.
The corresponding
output is printed
in the console
Data
corresponding to
the inclusion of
Portugal and
Albania and the
removal of Poland
from
participants_essi
are stored in the
data frame
data_fct
Figure/Table

Program
Output file
Note
Table 28
ME/Equilibria_
ESSI_22+Italy
+France_ed.R
Data
corresponding to
the inclusion of
Portugal and
Albania and the
removal of Poland
from
participants_essi
are stored in the
data frame
data_fct
References
Statista (2022). Länge der Grenzen von Russland zu den Nachbarstaaten (in
Kilometern). Data source: Central Intelligence Agency, The World Factbook.
Statista GmbH. https://de.statista.com/statistik/daten/studie/1306576/umfrage/laenge
der-grenzen-von-russland/
Central Intelligence Agency (2011). The World Factbook. Washington, DC.
https://www.cia.gov/the-world-factbook/
Sandler, Todd & Shimizu, Hirofumi (2014). NATO Burden Sharing
1999–2010: An Altered Alliance. Foreign Policy Analysis, 10(1), 43–60.
https://doi.org/10.1111/j.1743-8594.2012.00192.x
World Bank (2024). World Development Indicators. GDP (NY.GDP.MKTP.CD),
Military Expenditure (MS.MIL.XPND.CD), Population (SP.POP.TOTL). Data
retrieved via World Bank API on 08 November 2024. https://data.worldbank.org/
11