# Validating Game-Theoretic Models of Terrorism: Insights from Machine Learning

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conceptual Foundations

## 3. Machine Learning

#### 3.1. Classical and Other Regression Analysis

_{1},

**x**

_{1}), …(y

_{N},

**x**

_{N})}, any prediction function, d(

**x**

_{i}), maps the vector of input variables,

**x**, into the output variable (the number of terror attacks), y. An effective prediction algorithm seeks to define parameters that minimize an error function such as the mean absolute deviations or mean squared error, over the predictions. In linear regression models, d(

**x**

_{i}) is simply a linear function of the inputs. A linear model with the MSE error function yields the ordinary least squares (OLS) regression model:

**x**

_{i}) =

**x**

_{i}β is a linear function of the inputs.

**x**, to be an exponential function of a linear combination of the inputs expressed as:

**x**) = e

^{β}

**.**

^{x}#### 3.2. Artificial Neural Networks (ANNs)

#### 3.3. Regression Trees

- Binary splits to splits in the inputs that divide the subsample at each node, t;
- Criteria for splitting each node into additional “child” nodes, or including it in the set of terminal nodes, T*;
- A decision rule, d(
**x**), for assigning a predicted output value to each terminal node; - An estimate of the predictive quality of the decision rule, d.

#### 3.3.1. Boosting Algorithms

_{1}, …, f

_{M}) that progressively reweight the importance of each observation based on whether the previous classifier predicted it correctly or incorrectly. Modifications of the boosting algorithm for classification have also been developed for regression trees [21,22].

_{1}= (1/N, …, 1/N), suppose that our initial classifier, f

_{1}= T (single-tree CART, for example), is a “weak learner” in that the misclassification rate, $\widehat{R}\left(d\right)$ is greater than the desired maximum desired misclassification rate, $\tilde{R}$. Next, for all observations in the learning sample, recalculate the distribution weights for the observations as:

_{m}is a scaling constant that forces the weights to sum to one.

#### 3.3.2. Bootstrap Aggregating (Bagging)

^{(M)}}, from the learning sample with replacement to create M samples using only the observations from the learning sample. Each of these samples will contain N observations—the same as the number of observations in the full training sample. However, in any one bootstrapped sample, some observations may appear twice (or more), others not at all. Note that the probability that a single observation is selected in each draw from the learning set is 1/N. Hence, sampling with replacement, the probability that it is completely left out of any given bootstrap sample is (1 − 1/N)

^{N}. For large samples this tends to 1/e. The probability that an observation will be completely left out of all M bootstrap samples, then, is (1 − 1/N)

^{NM}. The bagging method then adopts the rules for splitting and declaring nodes to be terminal described in the previous section to build M classification trees.

#### 3.3.3. Random Forests

**x**, Θ

_{m}), m = 1, …, M}, where Θ

_{m}is a random vector specifying the observations and inputs that are included at each step of the construction of the decision rule for that tree. To construct a tree, the random forest algorithm takes to following steps:

- Randomly select n ≤ N observations from the learning sample;
- At the “root” node of the tree, select k ∈ K inputs from
**x**; - Find the split in each variable selected in (ii) that minimizes the mean square error at that node and select the variable/split that achieves the minimal error;
- Repeat the random selection of inputs and optimal splits in (ii) and (iii) until some stopping criteria (minimum improvement, minimum number of observations, or maximum number of levels) is met.

_{m}, of a random selection of n = N observations from the learning sample with replacement (and each observation having a probability of being selected in each draw equal to 1/N) and sets the number of inputs to select at each node, k, equal to the full length of the input vector, K so that all of the variables are considered at each node.

#### 3.4. Validation and Testing of Predictive Accuracy

## 4. Data

## 5. Results

#### 5.1. Predictive Quality

#### 5.2. Variable Importance

#### 5.3. The Nonlinear Relationship between Greater Security and Terrorism

_{k}conditional on the observed values of all of the other variables, (x

_{1,−k}, x

_{2,−k}, … x

_{n}

_{,−k}). Specifically, it plots the graph of the function:

## 6. Game-Theoretic Model Validation

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sandler, T.; Arce, D.G. Terrorism: A game-theoretic approach. Handb. Def. Econ.
**2007**, 2, 775–813. [Google Scholar] - Wasserstein, R.L.; Lazar, N.A. The ASA Statement on p-Values: Context, Process, and Purpose. Am. Stat.
**2016**, 70, 129–133. [Google Scholar] [CrossRef][Green Version] - Ward, M.; Greenhill, B.D.; Bakke, K.M. The Perils of Policy by p-value: Predicting Civil Conflict. J. Peace Res.
**2010**, 47, 363–375. [Google Scholar] [CrossRef][Green Version] - Basuchoudhary, A.; Bang, J.T.; Sen, T.; David, J. Identifying the Complex Causes of Civil War: Causal Interpretations of Machine Learning Technologies; Palgrave-MacMillan: Cham, Switzerland, 2021. [Google Scholar]
- Shughart, W.F., II. September 11, 2001. Public Choice
**2002**, 112, 1–8. [Google Scholar] [CrossRef] - Shughart, W.F., II. An Analytical History of Terrorism, 1945–2000. Public Choice
**2006**, 128, 7–39. [Google Scholar] [CrossRef] - Frey, B.S.; Luechinger, S. How to Fight Terrorism: Alternatives to Deterrence. Def. Peace Econ.
**2003**, 14, 237–249. [Google Scholar] [CrossRef][Green Version] - Faria, J.R.; Arce, D.G. Terror Support and Recruitment. Def. Peace Econ.
**2005**, 16, 263–273. [Google Scholar] [CrossRef] - Andreozzi, L. Rewarding Policemen Increases Crime. Another Surprising Result from the Inspection Game. Public Choice
**2004**, 121, 69–82. [Google Scholar] [CrossRef] - Zhuang, J.; Bier, V.M. Balancing terrorism and natural disasters—Defensive strategy with endogenous attacker effort. Oper. Res.
**2007**, 55, 976–991. [Google Scholar] [CrossRef][Green Version] - Enders, W.; Sandler, T. Distribution of Transnational Terrorism among Countries by Income Class and Geography after 9/11. Int. Stud. Q.
**2006**, 50, 367–393. [Google Scholar] [CrossRef] - Berman, E.; Laitin, D.D. Religion, terrorism and public goods: Testing the club model. J. Public Econ.
**2008**, 92, 1942–1967. [Google Scholar] [CrossRef][Green Version] - Bapat, N.A. Transnational terrorism, US military aid, and the incentive to misrepresent. J. Peace Res.
**2011**, 48, 303–318. [Google Scholar] - Enders, W.; Hoover, G.A. The nonlinear relationship between terrorism and poverty. Am. Econ. Rev.
**2012**, 102, 267–272. [Google Scholar] - Mullainathan, S.; Spiess, J. Machine learning: An applied econometric approach. J. Econ. Perspect.
**2017**, 31, 87–106. [Google Scholar] - Hand, D.; Mannila, H.; Smyth, P. Principles of Data Mining; MIT Press: Cambridge, MA, USA, 2001. [Google Scholar]
- Ripley, B.; Venables, W. R Package ‘nnet’ Version 7.3-12; R Foundation for Statistical Computing: Vienna, Austria, 2016; Available online: https://cran.r-project.org/web/packages/nnet/nnet.pdf (accessed on 28 June 2021).
- Breiman, L.; Friedman, R.A.; Stone, C.J.; Olshen, R.A. Classification and Regression Trees; Chapman and Hall: Boca Raton, FL, USA, 1984. [Google Scholar]
- Schapire, R.E. The strength of weak learnability. Mach. Learn.
**1990**, 5, 197–227. [Google Scholar] [CrossRef][Green Version] - Freund, Y.; Schapire, R.E. Experiments with a new boosting algorithm. ICML
**1996**, 96, 148–156. [Google Scholar] - Schapire, R.E. Using output codes to boost multiclass learning problems. ICML
**1997**, 97, 313–321. [Google Scholar] - Friedman, J.H. Greedy function approximation: A gradient boosting machine. Ann. Stat.
**2001**, 29, 1189–1232. [Google Scholar] [CrossRef] - Breiman, L. Bagging predictors. Mach. Learn.
**1996**, 24, 123–140. [Google Scholar] - Breiman, L. Random forests; Machine learning. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] - Gassebner, M.; Luechinger, S. Lock, stock, and barrel: A comprehensive assessment of the determinants of terror. Public Choice
**2011**, 149, 235–261. [Google Scholar] [CrossRef][Green Version] - Banks, A.S.; Wilson, K.A. Cross-National Time-Series Data Archive; Databanks International: Jerusalem, Israel, 2015; Available online: http://www.databanksinternational.com (accessed on 28 June 2021).
- Cruz, C.; Keefer, P.; Scartascini, C. Database of Political Institutions Codebook, 2015 Update (DPI2015); Inter-American Development Bank: Washington, DC, USA, 2016. [Google Scholar]
- PRS Group. International Country Risk Guide; PRS Group: East Syracuse, NY, USA, 2015; Available online: http://epub.prsgroup.com/products/international-country-risk-guide-icrg (accessed on 28 June 2021).
- Solt, F. The Standardized World Income Inequality Database*. Soc. Sci. Q.
**2016**, 97, 1267–1281. [Google Scholar] [CrossRef] - Reynal-Querol, M. Ethnicity, Political Systems, and Civil Wars. J. Confl. Resolut.
**2002**, 46, 29–54. [Google Scholar] [CrossRef][Green Version] - Mira, A.N. Moscow: Miklukho-maklai ethnological institute at the department of geodesy and cartography of the state geological committee of the soviet union. USSR
**1964**. [Google Scholar] - Basuchoudhary, A.; Bang, J.T.; Sen, T.; David, J. Predicting Hotspots: Using Machine Learning to Understand Civil Conflict; Rowman & Littlefield: Lanham, MD, USA, 2018. [Google Scholar]
- Carter, D.B. Provocation and the Strategy of Terrorist and Guerrilla Attacks. Int. Organ.
**2016**, 70, 133–173. [Google Scholar] [CrossRef][Green Version] - DeRouen, K., Jr.; Sobek, D. State capacity, regime type, and civil war. In What Do We Know about Civil Wars; Madon, T.D., Mitchell, S.M., Eds.; Rowman and LittleField: Lanham, MD, USA, 2016; pp. 59–74. [Google Scholar]
- Hendrix, C.S. Measuring state capacity: Theoretical and empirical implications for the study of civil conflict. J. Peace Res.
**2010**, 47, 273–285. [Google Scholar] [CrossRef] - Wilson, M.C.; Piazza, J.A. Autocracies and Terrorism: Conditioning Effects of Authoritarian Regime Type on Terrorist Attacks. Am. J. Politi- Sci.
**2013**, 57, 941–955. [Google Scholar] [CrossRef] - Varian, H.R. Big data: New tricks for econometrics. J. Econ. Perspect.
**2014**, 28, 3–28. [Google Scholar] - Basuchoudhary, A.; Razzolini, L. The evolution of revolution: Is splintering inevitable? Econ. Peace Secur. J.
**2018**, 13, 43–54. [Google Scholar] [CrossRef][Green Version] - De Mesquita, E.B. The quality of terror. Am. J. Political Sci.
**2005**, 49, 515–530. [Google Scholar] [CrossRef] - Aguiar, M.; Amador, M. Growth in the Shadow of Expropriation. Q. J. Econ.
**2011**, 126, 651–697. [Google Scholar] [CrossRef]

Variable | Source | Obs | Mean | Std. Dev. | Min. | Max. |
---|---|---|---|---|---|---|

Terror Attacks | GTD | 6411 | 86.88 | 375.81 | 0 | 10,701 |

Assassinations | CNTS | 5318 | 0.21 | 0.84 | 0.00 | 18.50 |

Cabinet Changes | CNTS | 5310 | 0.44 | 0.37 | 0.00 | 3.50 |

Demonstrations | CNTS | 5318 | 0.52 | 1.15 | 0.00 | 14.00 |

Effectiveness of Leg. | CNTS | 5297 | 1.74 | 0.94 | 0.00 | 3.00 |

Executive Changes | CNTS | 5310 | 0.19 | 0.28 | 0.00 | 3.00 |

Government Crises | CNTS | 5318 | 0.13 | 0.27 | 0.00 | 2.67 |

Guerrilla Warfare | CNTS | 5318 | 0.12 | 0.32 | 0.00 | 2.60 |

Purges | CNTS | 5318 | 0.03 | 0.13 | 0.00 | 2.50 |

Riots | CNTS | 5318 | 0.31 | 1.05 | 0.00 | 18.20 |

Strikes | CNTS | 5318 | 0.12 | 0.34 | 0.00 | 3.40 |

Changes in Veto Players | DPI | 4838 | 0.12 | 0.15 | 0.00 | 1.00 |

Checks on Power | DPI | 4831 | 2.52 | 1.60 | 1.00 | 17.00 |

Exec. Electoral Comp. | DPI | 4850 | 5.15 | 2.08 | 1.00 | 7.00 |

Executive Years in Office | DPI | 4859 | 7.93 | 7.68 | 1.00 | 45.00 |

Electoral Fraud | DPI | 4214 | 0.14 | 0.32 | 0.00 | 1.00 |

Government Frac | DPI | 4428 | 0.19 | 0.25 | 0.00 | 1.00 |

Government Herfindahl | DPI | 4428 | 0.82 | 0.25 | 0.02 | 1.00 |

Government Polarization | DPI | 4673 | 0.36 | 0.69 | 0.00 | 2.00 |

Legislative Frac. | DPI | 4419 | 0.46 | 0.30 | 0.00 | 1.00 |

Leg. Electoral Comp. | DPI | 4855 | 5.41 | 2.00 | 1.00 | 7.00 |

Military Executive | DPI | 4856 | 0.21 | 0.39 | 0.00 | 1.00 |

Opposition Frac | DPI | 3362 | 0.45 | 0.27 | 0.00 | 1.00 |

Plurality Voting | DPI | 3877 | 0.68 | 0.46 | 0.00 | 1.00 |

Proportional Rep. | DPI | 3474 | 0.58 | 0.49 | 0.00 | 1.00 |

Bureaucratic Quality | ICRG | 3376 | 2.11 | 1.19 | 0.00 | 4.00 |

Corruption | ICRG | 3376 | 3.08 | 1.35 | 0.00 | 6.00 |

Democratic Accountability | ICRG | 3376 | 3.64 | 1.62 | 0.00 | 6.00 |

Ethnic Tensions | ICRG | 3376 | 3.91 | 1.44 | 0.00 | 6.00 |

External Conflict | ICRG | 3376 | 9.48 | 2.22 | 0.00 | 12.00 |

Government Stability | ICRG | 3376 | 7.45 | 2.10 | 1.00 | 11.50 |

Internal Conflict | ICRG | 3376 | 8.61 | 2.62 | 0.03 | 12.00 |

Investment Profile | ICRG | 3376 | 6.94 | 2.34 | 0.08 | 12.00 |

Law and Order | ICRG | 3376 | 3.60 | 1.48 | 0.25 | 6.00 |

Military in Politics | ICRG | 3376 | 3.66 | 1.80 | 0.00 | 6.00 |

Religious Tensions | ICRG | 3376 | 4.54 | 1.35 | 0.00 | 6.00 |

Polity2 | Polity IV | 4520 | 1.16 | 7.26 | −10.00 | 10.00 |

Regime Durability | Polity IV | 4569 | 23.99 | 28.73 | 0.00 | 198.00 |

Ethnic Fractionalization | Reynal-Querol | 4749 | 0.45 | 0.28 | 0.01 | 0.96 |

Religious Fractionalization | Reynal-Querol | 4749 | 0.28 | 0.23 | 0.00 | 0.78 |

Income Inequality (Gini) | SWIID | 3350 | 38.52 | 9.87 | 16.49 | 69.35 |

Area | WDI | 6110 | 682,865 | 1,717,163 | 2 | 16,400,000 |

Off. Aid & Dev. Assistance | WDI | 4045 | 0.08 | 0.11 | −0.01 | 0.76 |

Arms Exports | WDI | 1703 | 0.01 | 0.08 | 0.00 | 1.50 |

Arms Imports | WDI | 3976 | 0.04 | 0.12 | 0.00 | 3.32 |

Education Spending | WDI | 3436 | 4.45 | 2.32 | 0.59 | 44.30 |

Foreign Direct Investment | WDI | 4602 | 2.80 | 4.72 | −32.30 | 72.50 |

Female Labor Force Part. | WDI | 3293 | 50.12 | 17.55 | 9.20 | 90.80 |

Fuel Exports | WDI | 3875 | 16.82 | 28.33 | 0.00 | 100.00 |

GDP per Capita | WDI | 4807 | 9560.35 | 16,016.19 | 65.64 | 141,000.00 |

Government Consumption | WDI | 4538 | 16.47 | 6.87 | 3.37 | 84.50 |

Health Spending | WDI | 2647 | 3.48 | 2.21 | 0.01 | 18.36 |

Immigrant Stock | WDI | 4975 | 8.07 | 13.75 | 0.03 | 86.80 |

Infant Mortality | WDI | 5103 | 48.11 | 40.72 | 2.18 | 174.00 |

Inflation | WDI | 4168 | 32.94 | 254.00 | −17.60 | 6522.40 |

Life Expectancy | WDI | 5074 | 64.79 | 10.58 | 24.30 | 82.50 |

Literacy Rate | WDI | 1549 | 73.42 | 23.01 | 10.90 | 100.00 |

Military Expenditures | WDI | 2995 | 2.74 | 3.03 | 0.09 | 48.60 |

Military Personnel | WDI | 3092 | 1.88 | 2.23 | 0.06 | 35.80 |

Population | WDI | 5190 | 30.94 | 116.87 | 8.82 | 1316.00 |

Population Growth | WDI | 5190 | 1.80 | 1.44 | −4.84 | 15.50 |

Portfolio Investment | WDI | 4000 | 0.01 | 0.16 | −0.02 | 4.88 |

Primary Enrollment | WDI | 4763 | 97.05 | 22.35 | 15.80 | 208.00 |

Secondary Enrollment | WDI | 4407 | 60.84 | 33.35 | 2.13 | 155.60 |

Social Contributions | WDI | 1203 | 17.11 | 15.02 | 0.00 | 59.97 |

Telephones | WDI | 5127 | 14.70 | 18.58 | 0.01 | 103.42 |

Tertiary Enrollment | WDI | 4135 | 18.62 | 19.36 | 0.00 | 99.20 |

Unemployment | WDI | 3007 | 9.03 | 6.78 | 0.20 | 59.50 |

Urban Population | WDI | 5190 | 50.33 | 24.51 | 4.18 | 100.00 |

Youth Dependency | WDI | 5000 | 62.07 | 23.94 | 19.44 | 114.40 |

Learning Sample | Test Sample | |||
---|---|---|---|---|

MSE | % Decrease | MSE | % Decrease | |

OLS Regression | 107,708.05 | 25.71% | 98,119.17 | 26.12% |

Poisson Regression | 151,539.85 | −4.52% | 139,385.78 | −4.96% |

Neural Network | 144,695.12 | 0.20% | 132,389.28 | 0.31% |

Regression Tree | 52,038.41 | 64.11% | 80,182.62 | 39.62% |

Boosting Predictor | 141,677.19 | 2.28% | 129,790.58 | 2.27% |

Bagging Predictor | 59,866.71 | 58.71% | 40,202.12 | 69.73% |

Random Forest | 54,271.19 | 62.57% | 38,504.85 | 71.01% |

Average of All Predictors | 74,564.39 | 48.57% | 76,391.30 | 42.48% |

Total MSE | 144,987.24 | 132,802.82 |

Variable | Tree | Bagging | Boosting | Forest | Average |
---|---|---|---|---|---|

Assassinations | 7.618 | 24.930 | 62.966 | 12.388 | 14.979 |

Guerrilla War | 2.677 | 10.735 | 30.698 | 9.436 | 7.616 |

Military Personnel | 15.482 | 4.166 | 0.000 | 2.555 | 7.401 |

Religious Frac | 12.386 | 4.761 | 0.000 | 3.218 | 6.788 |

Military Politics | 12.682 | 1.913 | 1.082 | 3.529 | 6.042 |

Health Spending | 3.765 | 4.390 | 2.499 | 3.548 | 3.901 |

Year | 1.882 | 5.704 | 0.000 | 3.888 | 3.825 |

Population | 0.947 | 3.568 | 0.394 | 5.562 | 3.359 |

Exec Yrs in Office | 6.441 | 1.940 | 0.000 | 1.315 | 3.232 |

Fuel Exports | 6.193 | 1.455 | 0.000 | 1.227 | 2.958 |

Dem Accountability | 5.222 | 1.243 | 0.000 | 1.411 | 2.625 |

Effectiveness of Leg | 0.000 | 3.104 | 0.000 | 3.041 | 2.048 |

Aid & Assistance | 2.528 | 0.973 | 0.000 | 1.826 | 1.775 |

Gini | 0.981 | 2.106 | 0.000 | 2.083 | 1.723 |

Tertiary Enrollment | 2.053 | 0.752 | 0.000 | 2.023 | 1.609 |

Female LFPR | 0.000 | 1.226 | 2.361 | 3.213 | 1.480 |

Portfolio Investment | 0.000 | 2.695 | 0.000 | 1.600 | 1.432 |

Area | 1.858 | 1.194 | 0.000 | 0.837 | 1.297 |

Arms Imports | 1.425 | 1.402 | 0.000 | 1.009 | 1.279 |

Strikes | 0.662 | 1.369 | 0.000 | 1.711 | 1.247 |

Ethnic Tension | 0.733 | 0.467 | 0.000 | 2.409 | 1.203 |

Checks | 1.702 | 1.248 | 0.000 | 0.615 | 1.188 |

Internal Conflict | 0.969 | 0.125 | 0.000 | 2.257 | 1.117 |

Telephones | 1.882 | 0.435 | 0.000 | 0.697 | 1.005 |

Law Order | 1.322 | 0.560 | 0.000 | 0.966 | 0.950 |

GDP pc | 0.235 | 0.842 | 0.000 | 1.736 | 0.938 |

Urban Population | 1.710 | 0.404 | 0.000 | 0.645 | 0.920 |

Ethnic Frac | 0.469 | 1.336 | 0.000 | 0.885 | 0.897 |

Polity 2 | 0.000 | 1.355 | 0.000 | 1.244 | 0.866 |

Investment Prof | 0.321 | 1.019 | 0.000 | 1.169 | 0.836 |

Legislative Frac | 1.425 | 0.532 | 0.000 | 0.549 | 0.835 |

Riots | 0.307 | 0.729 | 0.000 | 1.382 | 0.806 |

Primary Enrollment | 1.425 | 0.170 | 0.000 | 0.687 | 0.761 |

Arms Exports | 0.000 | 1.233 | 0.000 | 0.950 | 0.728 |

Demonstrations | 0.179 | 0.464 | 0.000 | 1.511 | 0.718 |

Unemployment | 0.000 | 0.813 | 0.000 | 1.310 | 0.708 |

Religious Tension | 0.000 | 0.300 | 0.000 | 1.601 | 0.634 |

Infant Mortality | 0.000 | 0.773 | 0.000 | 1.046 | 0.606 |

Secondary Enrollment | 0.000 | 0.848 | 0.000 | 0.765 | 0.537 |

Immigrant Stock | 0.016 | 0.672 | 0.000 | 0.816 | 0.501 |

Reg Durability | 0.248 | 0.547 | 0.000 | 0.609 | 0.468 |

Gov Consumption | 0.000 | 0.369 | 0.000 | 0.824 | 0.398 |

Gov Stability | 0.618 | 0.089 | 0.000 | 0.441 | 0.383 |

Corruption | 0.075 | 0.472 | 0.000 | 0.584 | 0.377 |

Life Expectancy | 0.000 | 0.242 | 0.000 | 0.889 | 0.377 |

Youth Dependency | 0.000 | 0.286 | 0.000 | 0.842 | 0.376 |

FDI | 0.000 | 0.372 | 0.000 | 0.719 | 0.363 |

Fraud | 0.346 | 0.106 | 0.000 | 0.421 | 0.291 |

Opposition Frac | 0.000 | 0.304 | 0.000 | 0.560 | 0.288 |

Inflation | 0.207 | 0.326 | 0.000 | 0.300 | 0.278 |

External Conflict | 0.259 | 0.140 | 0.000 | 0.428 | 0.276 |

Bureaucratic Qual | 0.000 | 0.277 | 0.000 | 0.501 | 0.259 |

Leg. Elec. Comp. | 0.248 | 0.192 | 0.000 | 0.295 | 0.245 |

Exec. Elec. Comp. | 0.000 | 0.262 | 0.000 | 0.465 | 0.242 |

Literacy Rate | 0.000 | 0.143 | 0.000 | 0.574 | 0.239 |

Population Growth | 0.000 | 0.394 | 0.000 | 0.302 | 0.232 |

Proportional Rep | 0.000 | 0.368 | 0.000 | 0.326 | 0.231 |

Social Contributions | 0.000 | 0.173 | 0.000 | 0.515 | 0.229 |

Military Expend | 0.167 | 0.212 | 0.000 | 0.277 | 0.219 |

Purges | 0.331 | 0.051 | 0.000 | 0.179 | 0.187 |

Education Spending | 0.000 | 0.243 | 0.000 | 0.304 | 0.182 |

Military Exec | 0.000 | 0.085 | 0.000 | 0.316 | 0.134 |

Government Herfindahl | 0.000 | 0.082 | 0.000 | 0.235 | 0.106 |

PluralityVoting | 0.000 | 0.093 | 0.000 | 0.196 | 0.096 |

Gov Polarization | 0.000 | 0.063 | 0.000 | 0.198 | 0.087 |

Government Frac | 0.000 | 0.093 | 0.000 | 0.087 | 0.060 |

Cabinet Changes | 0.000 | 0.028 | 0.000 | 0.085 | 0.038 |

Changes in Vetoes | 0.000 | 0.065 | 0.000 | 0.018 | 0.028 |

Executive Changes | 0.000 | 0.020 | 0.000 | 0.044 | 0.021 |

Government Crises | 0.000 | −0.050 | 0.000 | −0.191 | −0.080 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bang, J.T.; Basuchoudhary, A.; Mitra, A. Validating Game-Theoretic Models of Terrorism: Insights from Machine Learning. *Games* **2021**, *12*, 54.
https://doi.org/10.3390/g12030054

**AMA Style**

Bang JT, Basuchoudhary A, Mitra A. Validating Game-Theoretic Models of Terrorism: Insights from Machine Learning. *Games*. 2021; 12(3):54.
https://doi.org/10.3390/g12030054

**Chicago/Turabian Style**

Bang, James T., Atin Basuchoudhary, and Aniruddha Mitra. 2021. "Validating Game-Theoretic Models of Terrorism: Insights from Machine Learning" *Games* 12, no. 3: 54.
https://doi.org/10.3390/g12030054