Geoffrey HealGraduate School of Business

Columbia Universitygmh1@columbia.edu

Howard Kunreuther (kunreuther@wharton.upenn.edu) Center for Risk Management and Decision Processes

The Wharton SchoolUniversity of Pennsylvania

andVisiting Senior Research Scientist

Columbia University

You Can Only Die OnceInterdependent Security in an Uncertain World

Characteristics of the Problem

Non Additive Damages

(You can only die once)

Risk Faced by One Person Depends

on Actions Taken by Others

(Negative stochastic externalities)

Types of Problems

Investing in airline security

Making computer systems more secure against terrorist attacks. Protecting against chemical & nuclear accidents Making buildings more secure against attacks Investing in sprinklers to reduce the chances of apartment fires 

Avoiding divisional gambles that could bring entire firm into bankruptcy .

Nick Leeson, Singapore futures market & collapse of Baring’s Arthur Andersen brought into bankruptcy by Houston branch. 

Scenario Illustrating Interdependent Security

Be Careful (BC) Airlines considers installing baggage checking system for added protection.

Needs to balance the cost of this system with reduction in risk of explosion of luggage not only checked in with BC but also from bags of passengers checked in on other airlines & transferred to BC.

What is Interdependent Security?

An agent can protect itself against a risk by incurring an upfront investment cost

BC Airlines can invest in baggage security system to reduce

chance of bomb explosions

Investment in computer protection against viruses and hackers

An agent can be contaminated by others even if it is protected

BC Airlines can be contaminated by bags transferred from other airlines that were not inspected

Computer can be attacked by viruses from other computers

Interdependent Security Model Assumptions and Notation

Consider Two Airlines A1 and A2.

Y = income of each airline before any expenditure on security 

Probability contaminated bag is accepted and explodes in A i : p (p=.1)

Probability that contaminated bag gets accepted by A i and is transferred to another airline where it explodes : q (q=.2 )

Probability non-screened airline loads a checked bag with bomb: p + q

Loss if a bag explodes : L. (L=1000)

Investment Cost of Baggage Security System c (c=95)

 

Interdependent Security Model Expected Costs and Decisions

Expected Costs Associated with Investing (S) and Not Investing (N) in Baggage Security System  

AIRLINE 2 

S NS Y -95, Y -95 Y-295, Y -100

AIRLINE 1N Y -100, Y -295 Y -280, Y -280

Decisions  

If A2 has a security system (S) then it is worth A1 investing in one,   Expected losses reduced by pL= - 100

Cost of baggage security system. = 95  

If A2 does not invest in security (N) then A1 will not want to invest in one  Expected losses reduced by p (1-q)L - (280-200) = -80 Cost of baggage security system. = 95

Impact of Contamination if there are n Agents

Define X(n,0) to be the negative externalities to airline i if it invests in security and no other airline does

For investment in security to be dominant strategy you need

c < p [L- X(n,0)]

When is investment in security a dominant strategy with many agents and all the others have not protected themselves?

Airlines: c < p [e-q L] for any airline to invest in baggage security

Computers: no cost incentive (i.e. c <0 ) for a computer to protect itself against viruses or hackers

Tipping Behavior when there is contamination

Suppose the n airlines differ in the costs and/or risks they face.

Define Ej (n,0) as the negative externalities imposed by airline j on all

other airlines when no other airlines invest and airline j changes from investing to not investing in baggage security

Two Results

If by switching from N to S a single airline j can cause all others to switch from N to S it will be the one that with highest Ej(n,0).

If by switching from N to S a group of K airlines can cause all others to follow they will be the ones that have the K highest

Ej (n,0).

Types of Interventions(Internalizing Negative Externalities)

Insurance Not feasible under current system because insurer of agent i

does not pay for damage to agent j j i Monopolistic insurer provides premium reduction to agent i for

reduction in contamination to all other agents

Liability---This policy tool only works if contaminating agent is held liable for damage to others if it did not invest in protection

Regulations Importance of well-enforced codes and standards to ensure that cost-effective security measures are adopted

Types of Interventions(Internalizing Externalities)

Taxation—Can levy a tax of t dollars on any agent that did not invest in protection to encourage them to adopt security measures\

Coordinating mechanisms International Air Transport Association (IATA)---require

baggage security on all bags to be transferred to other airlines

Coops in NYC—Require that all buyers of apartments invest in sprinkler system as a condition for purchase

Social norms—role of friends and neighbors

Future Research Directions

Differential Costs and Risks

Nash equilibrium would be mixture of (S,S…N,N)

Prescriptive Questions

Do you tax some agents more because they have a greater chance of contaminating others?

Role of regulations (e.g. building codes, required baggage check-in)

Multi-Period and Dynamic Models

Importance of time horizon and discount rate

How do you get process of investing in security started?

Importance of developing sequential models of choice

Future Research Directions (cont.)

Behavioral Considerations

Misperceptions of risk

Myopia (i.e. short time horizons)

Importance of affect (e.g. worry, dread, anxiety)

Budget Constraints