Formal Models of Terrorism 1. Introduce formal methods and show how they apply to studies of terrorism. 2. Present examples from current research. 3. Discuss

Formal Models of TerrorismFormal Models of Terrorism

1.1. Introduce formal methods and show how Introduce formal methods and show how they apply to studies of terrorism.they apply to studies of terrorism.

2.2. Present examples from current research. Present examples from current research.

3.3. Discuss further research ideas using game Discuss further research ideas using game theoretic studies of terrorism.theoretic studies of terrorism.

4.4. Discuss the strengths and weaknesses of this Discuss the strengths and weaknesses of this approach. approach.

Understanding a Complex Understanding a Complex WorldWorld

The world is very The world is very difficult to understand – difficult to understand – complex, noisy.complex, noisy.

Think about your Think about your reaction to 9/11.reaction to 9/11.

Almost immediately, Almost immediately, people develop quick people develop quick explanations to help explanations to help them understand.them understand.

All of these explanations All of these explanations are essentially “models.”are essentially “models.”

Why Formalize?Why Formalize?

Mathematical reasoning attempts to, as best as possible, remove emotional responses and be precise in our definitions.

The mathematics is simply a reflection of the model’s logic – and using math is a way of determining what conclusions flow from the assumptions you make.

Formal models attempt to make an argument logically transparent – all of the assumptions are identified – and conclusions must flow from the assumptions.

Example of Informal Arguments Example of Informal Arguments Gone BadGone Bad……

Suppose I want to devise an argument to hold the Taliban accountable for supporting al Qaeda.

Assumption: States have monopoly on the legitimate use of force.

Implication: State support for any violent non-state actor, including terrorists, violates international law.

Conclusion: Therefore, by hosting al Qaeda, the Taliban violated international law.

But, my argument has a hidden But, my argument has a hidden implicationimplication……

The U.S. is also guilty!!!

U.S. hiring of Blackwater violates international law.

U.S. support for Northern

Alliance and Iraqi National Congress also in violation.

Formalizing arguments and making them explicit often exposes these sometimes unintended implications, or at least makes them transparent.

A Second Reason: UnobservablesA Second Reason: Unobservables

• Important to examine data to observe patterns.

• But, very important to develop theoretical explanations.

• Not enough to answer what is going on, it’s also important to know why.

• Especially because sometimes observations can be deceiving, particularly in an area like terrorism.

Example: Ku Klux Klan AttacksExample: Ku Klux Klan AttacksBorrowed from Borrowed from FreakonomicsFreakonomics

Years Lynchings1890-1899 11111900-1909 7911910-1919 5691920-1929 2811930-1939 1191940-1949 311950-1959 61960-1969 3

What’s Going On?What’s Going On?

• When Klan is weak, it lynches to appear powerful.

• If Klan is established, no one challenges it, so lynchings fall.

• Similar pattern in al Qaeda in Iraq’s level of violence today.

• Using formal models allow us to understand what we’re observing, but also what we’re not observing.

Rational Choice Models

1. Do not judge the morality of action.

2. Assumption that people have free will.

3. Individuals choose actions to achieve their goals: attempt to “maximize utility.”

4. Understanding that reality is simplified.

Rational Choice ModelsRational Choice Models According to rational choice, rationality According to rational choice, rationality

means you have ordered, transitive means you have ordered, transitive preferences. preferences.

Example:Example:Tenure > Join Blackwater > Tenure > Join Blackwater >

UnemploymentUnemployment

Tenure > BlackwaterTenure > Blackwater

Blackwater > UnemploymentBlackwater > Unemployment

Tenure > UnemploymentTenure > Unemployment

Given my laughable shooting skills, everyone Given my laughable shooting skills, everyone would be better off if I got tenure!would be better off if I got tenure!

Same with Application to Same with Application to Terrorism: Zarqawi’s PreferencesTerrorism: Zarqawi’s Preferences

1.1. Kill Americans. Kill Americans.

2.2. Kill Shi’ites. Kill Shi’ites.

3.3. Kill Sunni collaborators. Kill Sunni collaborators.

Preferences are clearly homicidal, Preferences are clearly homicidal, and and

appear crazy.appear crazy.

Doesn’t matter, as long as they are Doesn’t matter, as long as they are ordered ordered

and transitive, Zarqawi can be and transitive, Zarqawi can be considered considered

rationalrational..

The Challenge: Making Decisions The Challenge: Making Decisions Under RiskUnder Risk

Now you need to make decisions to realize these Now you need to make decisions to realize these outcomes. The problem, however, is that you outcomes. The problem, however, is that you don’t have perfect foresight. don’t have perfect foresight.

In almost all aspects of international politics, In almost all aspects of international politics, individuals make decisions under risk.individuals make decisions under risk.

ExampleExample: If you attack Afghanistan, you : If you attack Afghanistan, you have a 60% chance of killing or capturing have a 60% chance of killing or capturing bin Laden. bin Laden.

To be rational, you make decisions by assigning To be rational, you make decisions by assigning utilities (numerical values) to outcomes and utilities (numerical values) to outcomes and incorporate risk.incorporate risk.

Bush Preference ProfileBush Preference Profile

Kill bin Laden > Bombing Campaign > Fail to Capture bin Kill bin Laden > Bombing Campaign > Fail to Capture bin LadenLaden

11 0 0 -1 -1

If Bush invades Afghanistan, he has a 60% chance of If Bush invades Afghanistan, he has a 60% chance of killing bin Laden and getting a value of 1.killing bin Laden and getting a value of 1.

But, there is also a 40% chance that the operation will fail, But, there is also a 40% chance that the operation will fail, resulting in a value of -1. resulting in a value of -1.

If he only engages in a bombing campaign, he won’t If he only engages in a bombing campaign, he won’t capture bin Laden, but he won’t fail. He therefore gets a capture bin Laden, but he won’t fail. He therefore gets a value of 0 for certain.value of 0 for certain.

Expected Utility CalculationExpected Utility Calculation

EUEUBUSHBUSH(Invasion) = (.6)*(1) + (.4)*(-1)(Invasion) = (.6)*(1) + (.4)*(-1)

= .2= .2

EUEUBUSHBUSH (Bombing Campaign Only) = 0 (Bombing Campaign Only) = 0

Since .2 > 0, Rational G.W. attacksSince .2 > 0, Rational G.W. attacks..

Understanding Strategic Understanding Strategic InteractionInteraction

Game Theory is the study of strategic interaction Game Theory is the study of strategic interaction among rational individuals.among rational individuals.

If I think you are going to attack, how does this If I think you are going to attack, how does this affect my decision-making?affect my decision-making?

If we know Bush will attack, how does this affect If we know Bush will attack, how does this affect bin Laden’s decision?bin Laden’s decision?

9/11 Game:9/11 Game: Bin Laden and BushBin Laden and Bush

Attack Do Not Attack

Bush Invades Bush Bombs

Capture binLaden 60%

Miss bin Laden 40%

Bin Laden: 1; Bush: 0


Bin Laden: -1; Bush: 1

Bin Laden: 2; Bush: -1

What Does Bin Laden Do, Given What Does Bin Laden Do, Given Bush’s Actions?Bush’s Actions?

We know from the previous calculation that Bush We know from the previous calculation that Bush will invade. will invade.

Bin Laden can therefore anticipate an American Bin Laden can therefore anticipate an American invasion in response to his attack.invasion in response to his attack.

So, EUSo, EUBINLADENBINLADEN (Attack) = .6*(-1) + .4*(2) (Attack) = .6*(-1) + .4*(2)

= .2= .2 Compare to EUCompare to EUBINLADENBINLADEN(No Attack) = 0(No Attack) = 0

Since .2 > 0, bin Laden Attacks. Since .2 > 0, bin Laden Attacks.

What do the Numbers Mean?What do the Numbers Mean?

The “numbers” can be seen as The “numbers” can be seen as variablesvariables..

For example, let us consider p, or the probability For example, let us consider p, or the probability of victory.of victory.

The value of p is a function of the U.S. The value of p is a function of the U.S. investment in its military and counterinsurgency investment in its military and counterinsurgency capability. capability.

This is public information, bin Laden can get it!!!This is public information, bin Laden can get it!!!

Since p is a probability, U.S. kills bin Laden with Since p is a probability, U.S. kills bin Laden with probability p and fails to do so with probability probability p and fails to do so with probability (1-p). (1-p).

9/11 Game:9/11 Game: Bin Laden and BushBin Laden and Bush

Attack Do Not Attack

Bush Invades Bush Bombs

U.S. Wins p

U.S. Loses 1-p



Bin Laden: -1; Bush: 1

Bin Laden: 2; Bush: -1

The Model in Strategic FormThe Model in Strategic Form

Bush

Invade Bomb

Attack p(-1)+.(1-p)(2); 1

Bin Laden p(1)+(1-p)(-

1) 0

~Attack 0 0

1 1

Equilibrium: A set of rational best replies.

We now logically prove when 9/11 occurs, given the value of p.

EquilibriumEquilibrium

Bush

Invade Bomb

Attack p(-1)+.(1-p)(2); 1

Bin Laden p(1)+(1-p)(-

1) 0

~Attack 0 0

1 1

Bin Laden’s equilibrium strategy is to attack if p < 2/3.Bush’s equilibrium strategy is to attack if p > 1/2.

Why is this Useful?Why is this Useful?

This was a very simple model, but we still learned something.

Game theory often does illustrate conclusions that conventional wisdom has already uncovered.

But, game theory frequently also leads to conclusions that are not necessarily obvious.

If the assumptions that led to the obvious conclusions are correct, then the non-obvious conclusions should also be correct.

Application #1: Counter-terrorismApplication #1: Counter-terrorism

Problems with U.S. Problems with U.S. counter-terrorism counter-terrorism spending are well spending are well documented. documented.

Terrorists can observe Terrorists can observe this, and therefore this, and therefore probably think it’s a probably think it’s a good idea to attack good idea to attack cities. cities.

But, if this is true, why But, if this is true, why has there not been has there not been another 9/11 style another 9/11 style attack?attack?

Public information says Public information says city security may be city security may be inadequate, while pork is inadequate, while pork is being spent on other being spent on other areas. areas.

But, appropriations for But, appropriations for security done in previous security done in previous fiscal years, meaning fiscal years, meaning that city security is that city security is already upgraded. already upgraded.

If terrorists think the If terrorists think the facilities are facilities are unprotected, they will unprotected, they will still attack – and they still attack – and they will be caught! will be caught!


This mixing of signals This mixing of signals maximizes protection maximizes protection with a limited budget. with a limited budget.

Unfortunately, at some Unfortunately, at some point, terrorists will point, terrorists will adjust their strategies. adjust their strategies.

Therefore, a key part of Therefore, a key part of counter-terrorism is counter-terrorism is mixing signals to mixing signals to minimize these minimize these successful attacks – successful attacks – game theory can tell you game theory can tell you how.how.


Application #2: Peace ProcessesApplication #2: Peace Processes

Both governments and Both governments and terrorists claim to want terrorists claim to want peace – but peace peace – but peace processes are rare. processes are rare.

Often times – they keep Often times – they keep fighting, even though fighting, even though there appears to be no there appears to be no end in sight. end in sight.

Why does this occur?Why does this occur?

Bargaining theory Bargaining theory identifies what is known identifies what is known as a commitment as a commitment problem. problem.

Arafat

Fulfill Renege

Fulfill 5 0

Barak 5 10

Renege 10 0

0 0

Both sides prefer fulfilling their agreement to watching the agreement fail, but…


Arafat

Fulfill Renege

Fulfill 5 -1

Barak 5 10

Renege 10 0

-1 0

Since both sides fear that the other will renege, both sides have incentives to renege!! So, there is no peace agreement!


Application #3: State SponsorshipApplication #3: State Sponsorship

One of my main areas of interest is state One of my main areas of interest is state sponsorship of terrorism.sponsorship of terrorism.

From Bruce Hoffman, Daniel Byman, and From Bruce Hoffman, Daniel Byman, and others, we know that this often ends badly for others, we know that this often ends badly for the sponsor.the sponsor.

Sponsor might want to make peace, but Sponsor might want to make peace, but terrorists want to keep fighting.terrorists want to keep fighting.

Lots of examples: US & Lots of examples: US & mujahedeenmujahedeen; India & ; India & LTTE; Pakistan & Kashmiris.LTTE; Pakistan & Kashmiris.

Puzzle of State SponsorshipPuzzle of State Sponsorship

But, if we know that sponsorship often ends But, if we know that sponsorship often ends badly, badly, so should the sponsor.so should the sponsor.

So, why would a sponsor support a So, why would a sponsor support a terrorists if it knew that doing so would terrorists if it knew that doing so would eventually be costly?eventually be costly?

If we follow the logic, the empirical expectation If we follow the logic, the empirical expectation is that we should not observe state supported is that we should not observe state supported terrorism.terrorism.

But, the puzzle is that we still do…why?But, the puzzle is that we still do…why?

We can address this using a ModelWe can address this using a Model

HOST

TARGET

HOST

TARGET

Host SupportsInsurgency

Host SuppressesInsurgency, InsurgencyResists

Target OffersBribe

Host AcceptsBribe, InsurgencyResists

Target Attacks

Target Capitulates

Host Rejects Bribe

Figure 2. Insurgency and International Crisis

UncertaintyUncertainty

Host is unaware of the target’s payoff for attacking – it cannot perfectly predict if the target will escalate in its final move.

If the host opposes the militants, it faces the risk of destabilization (γ).

The host holds onto power with probability γ, and loses power with probability (1- γ).

However, if a deal is reached, the target provides aid to the host such that the value of γ increases.

Model Interpretation: Support for Model Interpretation: Support for Hoffman and BymanHoffman and Byman

Catalyst for war is often Catalyst for war is often sponsors that lose sponsors that lose control over their control over their terrorists. terrorists.

Weak states cannot Weak states cannot credibly agree to credibly agree to disarm their terrorists. disarm their terrorists.

If target is credible and If target is credible and sponsor cannot control sponsor cannot control its terrorists, conflict its terrorists, conflict spreads into war.spreads into war.

Empirical examples: Empirical examples: Taliban & al Qaeda; Taliban & al Qaeda; Lebanon & PLO; Lebanon & PLO; Laurent Kabila & Laurent Kabila & interhamweinterhamwe..

But, Something New…But, Something New…

What if the target cannot credibly threaten What if the target cannot credibly threaten an attack? Then, target has no choice but to an attack? Then, target has no choice but to bargain.bargain.

If the sponsor appears vulnerable, the If the sponsor appears vulnerable, the sponsor is going to demand enormous sponsor is going to demand enormous concessions.concessions.

In other words, the weaker the sponsor In other words, the weaker the sponsor appears, the more the sponsor gains!!!appears, the more the sponsor gains!!!

This is why states support terrorism, even if This is why states support terrorism, even if there is some probability that it will there is some probability that it will backfire.backfire.

PakistanPakistan

Despite all evidence to Despite all evidence to the contrary, Pakistan is the contrary, Pakistan is considered a loyal ally in considered a loyal ally in War on Terror.War on Terror.

The reason is that Bush The reason is that Bush prefers keeping prefers keeping Musharraf in power than Musharraf in power than allowing Pakistan to allowing Pakistan to collapse.collapse.

Result: sponsorship is Result: sponsorship is profitable for profitable for Musharraf!!!Musharraf!!!

Saudi ArabiaSaudi Arabia According to many in According to many in

U.S. government, Saudi U.S. government, Saudi Arabia does not appear Arabia does not appear fully cooperative. fully cooperative.

But, Bush But, Bush Administration insists Administration insists that Saudi Arabia is a that Saudi Arabia is a loyal ally.loyal ally.

Why? A Saudi collapse Why? A Saudi collapse would be would be devastatingdevastating for the U.S.for the U.S.

If the target cannot If the target cannot credibly attack, host credibly attack, host states have incentives to states have incentives to appear as weak as appear as weak as possible!!!possible!!!

What did the Model Teach Us?What did the Model Teach Us?

We see the traditional argument, but we also We see the traditional argument, but we also learn something new…learn something new…

If it appears that the sponsor will lose control, If it appears that the sponsor will lose control, and the target prefers keeping the sponsor in and the target prefers keeping the sponsor in power…power…

Therefore, even if there is a risk that Therefore, even if there is a risk that terrorists will turn on them later, support for terrorists will turn on them later, support for terrorism can provide bargaining power. terrorism can provide bargaining power.

Game Theory and Questions of Game Theory and Questions of TerrorismTerrorism

1.1. How do terrorists mobilize? How do terrorists mobilize?

2.2. How do terrorists design their organizations?How do terrorists design their organizations?

3.3. When and where do terrorists attack? When and where do terrorists attack?

4.4. What are the optimal counter-terrorism policies What are the optimal counter-terrorism policies states can adopt?states can adopt?

Game Theory and Questions of Game Theory and Questions of TerrorismTerrorism

5.5. When should states negotiate with terrorists, When should states negotiate with terrorists, and when are such negotiations successful?and when are such negotiations successful?

6.6. When do terrorists move abroad in search of When do terrorists move abroad in search of international alliances? international alliances?

7.7. How does terrorism spread to international How does terrorism spread to international war?war?

8.8. How can states design institutions to minimize How can states design institutions to minimize terrorism?terrorism?

Shortcomings of Rational ChoiceShortcomings of Rational Choice

Not descriptively accurate – nobody actually Not descriptively accurate – nobody actually calculates stuff.calculates stuff.

Assumes away preferences, therefore cannot Assumes away preferences, therefore cannot answer very important question such as why answer very important question such as why terrorists have the preferences that they do. terrorists have the preferences that they do.

Models can either be too simple or overly Models can either be too simple or overly complex. complex.

But, despite these limitations, I believe this But, despite these limitations, I believe this method is very effective, particularly when method is very effective, particularly when tested empirically. tested empirically.

Documents

Formal Models of Terrorism 1. Introduce formal methods and show how they apply to studies of terrorism. 2. Present examples from current research. 3. Discuss