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Journal of Security EducationPublication details including instructions forauthors and subscription informationhttpwwwtandfonlinecomloiwzse20

Using Game Theory in Managingthe Risks of TerrorismBrian Seymour BA a ba Boston University USAb John Jay College of Criminal Justice MastersProgram in Protection Management USAPublished online 20 Oct 2008

To cite this article Brian Seymour BA (2004) Using Game Theory in Managingthe Risks of Terrorism Journal of Security Education 11 95-105 DOI 101300J460v01n01_09

To link to this article httpdxdoiorg101300J460v01n01_09

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STUDENT PAPERS

Using Game Theoryin Managing the Risks of Terrorism

Brian Seymour BA

ABSTRACT The purpose of this paper is to explore how innovativeideas based on game theory can be useful to security professionals andgovernments in managing the risks posed by a terrorist attack [Articlecopies available for a fee from The Haworth Document Delivery Service 1-800-HAWORTH E-mail address ltdocdeliveryhaworthpresscomgt Website lthttpwwwHaworthPresscomgt copy 2005 by The Haworth Press Inc All rights reserved]

KEYWORDS Game theory probability Nash Equilibrium terrorismminimax criterion substitution strategies

PROBABILITY AND SECURITY MANAGEMENT

One day in a class called Contemporary Issues in Security Manage-ment the professor proposed a situation and asked a question Studentswere told to imagine they were the Chief Security Officer of a large cor-

Brian Seymour BA (Psychology at Boston University) is a Graduate Student atthe John Jay College of Criminal Justice Masters Program in Protection Management

Journal of Security Education Vol 1(1) 2005httpwwwhaworthpresscomwebJSE

2005 by The Haworth Press Inc All rights reservedDigital Object Identifier 101300J460v01n01_09 95

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poration and the Chief Executive Officer asked for an immediate an-swer to the questions of whether it was prudent to purchase terrorisminsurance Everyone in the class that raised their hand said it was neces-sary However I disagreed Terrorism insurance is very expensive andeven though the result of a terrorist attack is usually severe the proba-bility of it happening is so low it does not warrant the expense Re-sources could be better spent on managing other risks that are morelikely to occur

Probability is a very important issue for a security professional Fi-nite resources must be allocated to manage risks that have the great-est potential to harm as well as having a high probability ofoccurring A security manager interacts with human resource depart-ments upper management and financial officers in day-to-day opera-tions These managers can have a tremendous input in how defensiveresources are allocated However a security manager must keep inmind that people in general are not good at judging risks especially onesassociated with dangers In 2002 two men Vernon Smith and DanielKahneman won the Noble Prize in economics based on their workshowing how people are not wise at assessing probability

Recently some people in the security and risk management fieldshave advocated using principles based on game theory to try and modelor predict the probability of a terrorist attack These innovative ideascould be useful to a security manager defending targets against a possi-ble terrorist attack

JOHN NASHrsquoS GAME THEORY

At age 21 John Nash wrote a 27-page dissertation later called theNash Equilibrium His work was an extension of game theory that wasdeveloped by John von Neumann and Oskar Morgenstern in 1944Game theory strives to predict human behavior in non-cooperativecompetitive interactions It uses mathematical propositions to predictthe outcome when players have conflicting interest

Game theory can provide a useful framework for analyzing bargain-ing bidding and negotiation Modern game theory has been adopted infinancial markets environmental studies public policy-making con-flict resolution and peace negotiations Nashrsquos theory has had an effecton fields of study that are centered around competitive behavior includ-ing economics political science military science missile defense labormanagement negotiations consumer price wars currency speculations

96 JOURNAL OF SECURITY EDUCATION

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sports and auctions Some companies in the insurance industry are us-ing game theory to analyze the risk of future terrorist attacks by model-ing possible responses of terrorist groups to increased security andcounter-intelligence efforts

ADVANCED TECHNIQUESFOR MODELING TERRORISM RISK

What does game theory have to do with contemporary issues in secu-rity management Imagine a security manager protecting multiple siteswith different strategic and monetary values This manager could be thehead of security for a multi-national corporation that has manufacturingand distribution plants all over the world or a security manager oversee-ing several sites in New York City The security manager has three as-sumptions about defending the multiple targets against the threat of apossible terrorist attack First all the targets have some risk of being at-tacked and need to be defended Second the more valuable a target is themore likely it is to be attacked Third the risk of a successful attack in-creases the more valuable a target is According John A Major author ofldquoAdvanced Techniques for Modeling Terrorism Riskrdquo these assump-tions are wrong Major is a senior vice president for Guy Carpenter ampCompany Inc an insurance brokerage firm His paper elaborates on aspeech he gave at the National Bureau of Economic Research InsuranceGroup in February 2002 The paper draws on several theories includ-ing game theory in an attempt to model the risk posed by terrorists Thepaper contains formulas that he uses to draw conclusions The follow-ing is a summary of some of Majorrsquos points

The events of September 11th showed how a terrorist attack can nowbe classified as a catastrophic loss event The monetary damages of over$40 billion and the death toll of more than 3000 are more severe thanthe damage of some of the countryrsquos worst natural disasters (HurricaneAndrewndash$20 billion 40-60 people killed The Northridge earthquakendash$125 billion approximately 25 people killed) Modeling terrorism riskhas similarities with other forms of catastrophic risk however key dif-ferences make modeling terrorism more difficult According to Major

Terrorism risk shares features with other forms of catastrophicrisk including a time series of historical events yet goes beyondthem with an extra layer of impenetrability Defensive studies ofterrorism risk resemble analysis of complex engineering systems

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(nuclear power plants satellite launches etc) A particular sce-nario can be analyzed in terms of the probability of failure of criti-cal subsystems However unlike natural disasters it featureshuman intelligence and unlike industrial disasters it features hu-man intent

Before September 11th insurers did not consider the human elementin catastrophic risk modeling In a statement on his paper Major saidldquoStorms will not change course after you build a seawall to protect resi-dents on the coast But terrorists will change strategies techniques andtargets given the defenses put in place by a countryrdquo In order to have amodeling structure that is of any use to the insurance or security indus-try simple probability is not sufficient

Two theories that Major proposes could be useful to a security man-ager First the probability of a successful attack decreases with an in-crease in applied defensive resources Therefore the security managershould use all defense resources No benefit accrues in holding back be-cause according to Major ldquo[a] quantity of unused resources could beapplied to reduce the success probability and hence the expected loss ofat least one targetrdquo According to this idea a security manager shouldnot save any defensive resources for the proverbial rainy day

The second point of use is a defensive strategy that is a result of theldquominimax criterionrdquo This criterion refers to the assumption in his for-mulas that the attacker wants to maximize the total expected loss and thedefender wants to minimize it Assuming the defender does not knowwhich targets will be chosen by the attacker the defensive strategyshould be to minimize the expected loss of the worst case scenario re-gardless of which site is selected for attack To do this resources shouldbe shifted from lower expected loss targets to higher expected loss tar-gets Less valuable targets can be left undefended because even if an at-tack is 100 successful the loss would be less than the loss from a morevaluable target being hit

A security manager should use all resources to defend the targets thathave the greatest possibility of producing a large loss Spreading thewealth or covering all your bases is not desirable In his paper Majorquotes C J Hitch [in Quade] who states that some of the conclusions oftheory concerning defending targets are counterintuitive

Suppose you have your defenses deployed as well as you canNow you get more defenses How do you deploy them Well myintuition told me (and so did most peoplersquos) that you deploy them


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mainly to protect additional targets that you did not previouslyhave enough stuff to defend Game theory says no You use addi-tional defenses mainly to increase the defense of targets alreadydefended In fact over a wide range the more you have the moreyou concentrate it (Major 2002)

These innovative ideas may contradict established beliefs such asyour defense is only as strong as your weakest link Terrorists want tokill and destroy but also want to instill fear in those not directly affectedby the attack According to Major not all targets will be at risk Terror-ists will look at some sites and determine that there is no value in attack-ing These targets do not need any defense In direct contradiction to thethree afore mentioned assumptions Major states

The probability of an attack being successful also goes down withthe higher value of the target not up so the more valuable tar-gets are actually safer given that the defenses in place are ade-quate and both the would-be terrorists and the defenders give thesame measure of importance to the target If the defenses arenrsquotarranged correctly then the attacker will look for chinks in the ar-mor That might be a better description of where we are today(Best Wire 2002)

HOMELAND DEFENSE RESOURCE ALLOCATION

If security analysts find Majorrsquos line of thinking reasonable theywould be disappointed to see how the Department of Homeland Secu-rity and Congress are allocating resources for national protection Todate more than 3 billion dollars have been distributed New York hasreceived the most with about $321 million and California comes in sec-ond with $304 million This would seem to fit the game theory notionthat resources should go to targets highly valued by terrorists Howeverthe Associated Press (2003) analyzed allocations based on populationand determined that 12 states received more money than New York on aper capita basis Wyoming received $177 million which works out tonearly $36 per person New York by comparison received $17 per per-son and California $9 According to Arnold of the Associated PressldquoWashington DC has received $7310 per person more than anystate But even the nationrsquos capital is not the per capita championAmerican Samoa a US territory 2300 miles south of Hawaii received

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$54 million in homeland security funds or $9440 for each of its57291 residentsrdquo According to Carolyn Maloney Democratic Repre-sentative from New York ldquo70 percent of homeland security grants havebeen distributed under a formula that is entirely unrelated to where theterror threat is The number could rise to 83 percent next year under leg-islation being considered in Congress Our effort to protect the mostlikely targets of terrorism is moving backwardrdquo (Arnold 2003)

The current formula for distribution contradicts the suggestions pro-posed by Major that resources should be concentrated on high-risk tar-gets at the expense of spending resources on targets that have a lowexpected loss amount in the event of a successful attack

COMMERCIAL APPLICATIONS

John A Major is not alone in his use of game theory to model terror-ism risk In 2002 Risk Management Solutions (RMS) introduced mod-els based on John Nashrsquos theory RMSrsquos ldquoUnderstanding and ManagingTerrorism Riskrdquo is designed to assist property owners insurers and re-insures and other industries in quantifying the risk from catastrophicterrorist attacks It was developed with the help of experts in terrorismweapons systems and security from the United States and other coun-tries Dr Gordon Woo a mathematician who was the architect of theRSM model suggests that the probability of an attack and targets cho-sen by terrorists can be modeled by understanding the operational be-havioral characteristics of terrorist organizations According to Wooal-Qaeda operates ldquoin a similar way to the flow of water which seeksthe path of least resistance the flow of al-Qaeda activity is towardsweapons and targets that present the lowest technical logistical and se-curity barriers to mission successrdquo (Newswire 2002) However ac-cording to Dr Rohan Gunaratna a key adviser to Dr Woo ldquoOne cansafely predict that al-Qaeda will continue to stage spectacular land seaand air attacks in the future especially against symbolic or high-profiletargetsrdquo (Newswire 2002) The enemy seems to have two strategies thatcontradict According to Dr Woo

Game theory helps us model the implications of the complex dy-namics between these conflicting factors On one hand we haveal-Qaedarsquos desire to maximize the utility of their attacks and onthe other hand we have to consider their rational response tostepped-up security and counter-intelligence efforts and the con-


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straints of their technological and logistical capacities A tradi-tional probabilistic approach such as used for modeling naturalcatastrophes is simply not up to the challenge

According to Hemant Shah president and CEO of RMS clients are ad-vised to use this model as part of a comprehensive risk management strat-egy ldquoFirst and foremost we recommend that our clients build their riskmanagement infrastructure on a foundation of data data and more data In-surers should track their exposures across all lines of business location-by-location and understand and mitigate undue concentration of riskrdquo

Shahrsquos point on the importance of data cannot be stressed enough Inhis paper Major quotes Dr Woo who is the chief architect for the RSMmodel According to Woo ldquoAny probabilistic framework for quantify-ing terrorism risk however logically designed will ultimately have toinvolve a measure of expert judgmentrdquo (Major 2002)

A security manager who faces the threat of terrorism should be aware ofthe importance of collecting intelligence in the form of data on their sitesThey should take advantage of expert judgment especially in the area ofinnovative probability of modeling terrorism risk If something can bemodeled it can be measured If it can be measured it may be controlled

SUBSTITUTION STRATEGIES AND COOPERATION

Using game theory to deal with the threat of terrorism is not only use-ful for the insurance industry but also for governments Todd Sandlerprofessor of international relations at the University of Southern Cali-fornia has been using game theory in the study of transnational terror-ism for more than 20 years According to Sandler terrorists have anadvantage over governments because ldquoTerrorists take a long-term viewof their struggle and see interaction with other groups as continualwhile most governments take a short-term view of the terrorist threatand do not necessarily see cooperation with other governments as con-tinualrdquo (Marano 2003)

According to Sandler terrorists choose targets carefully yet theymake it seem as if it is random This is done to raise fear and cause ter-ror As governments strengthen some targets terrorists look for easiersofter targets Sandler states

An important terrorist gambit as analyzed by game theory is find-ing substitution strategies For example when metal detectorswere placed in most airports skyjackings declined but hostage

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taking in unprotected facilities increased The fortification of USembassies and missions reduced attacks against the structures butmore diplomats and military personnel were assassinated outsidethe protected compounds (Marano 2003)

A substitution strategy is an important concept for a security man-ager If the front door is secure and this is known to the attackers theywill probably look for a softer target The defender should try to antici-pate in a proactive fashion where the next move will be Then resourcescan be applied accordingly

Cooperation is an important part of fighting terrorists Terrorists co-operate because they face a stronger opponent and they see the struggleas continuing forever According to Sandler ldquoInternational cooperationis required in terms of deterrence pre-emption intelligence and pun-ishment of terrorists As long as governments place more weight ontheir autonomy than on the threat terrorists will continue to probe thelsquoseamsrsquo of sovereigntyrdquo (Marano 2003)

Cooperation is also very important for private companies as well as thefederal government Security managers should take advantage of organiza-tions such as the Oversees Security Advisory Committee (OSAC) theInternational Security Managers Association (ISMA) and ASIS Inter-national to build a network of cooperating interests That can be usefulin the process of benchmarking by which leaders in different industriescompare and contrast policy programs and procedures Benchmarkingis extremely important when companies are treading new ground suchas the fight against terrorism Security managers must realize that evenrival companies can work together for a common good because theyshare the same risks and dangers

LIMITATIONS OF GAME THEORY

There has been an ongoing debate on whether game theory and theNash Equilibrium have any usefulness that started before John Nashwon the Nobel Prize Robert Matthews highlights this in his reference toSylvia Nasarrsquos biography of John Nash called A Beautiful Mind

As Nasar reveals in her book the real worth of Nashrsquos work was stillbeing disputed by the members of the Nobel Committee just hoursbefore the vote on whether Nash and two other game theorists shouldwin the 1994 Nobel Prize for Economics According to Nasar one


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committee member dared to ask if there was one shred of empiricalbacking for Nashrsquos work A bitter row ensued followed by the bal-lot in which Nash and the other game theorists allegedly just scrapedenough votes to take the prize (Matthews 2002)

The debate continues to this day on whether game theory can be use-ful to predict real world situations According to London (2002) thereare those that think game theory has little use in determining the proba-bility of real world events

ldquoThe academic literature is strangely silent on this pointrdquo says ScottArmstrong marketing professor at Wharton Business School at theUniversity of Pennsylvania After conducting an exhaustive reviewof the literature however Professor Armstrong concluded that hewas ldquounable to find any evidence to directly support the belief thatgame theory would aid predictive abilityrdquo

Proponents of game theory disagree with the idea that game theory isnot useful in predicting real world outcomes Robert Wilson a profes-sor of economics at Stanford Business School believes that game theorypoints to a number of possible outcomes ldquoGame theory does not offerany specific answers to any specific situation It says something likelsquothese are the things to take into accountrsquordquo (London 2002)

Ideas in game theory can be helpful in analyzing a situation involvinga terrorist attack however they should not be seen as a definitive blue-print for how a security manager should act Saul I Gass professoremeritus at the University of Marylandrsquos Robert H Smith School ofBusiness explains ldquo[for] many circumstances game theory does not re-ally solve the problem at hand Instead it helps to illuminate the tasks byoffering a different way of interpreting the competitive interactions andpossible resultsrdquo (Gass 2003)

CONCLUSION

Game theory does not offer definitive outcomes to competitive situa-tion involving terrorists and security managers However it is one ofmany tools that can be useful for a security manager when making deci-sions regarding defenses against terrorist attacks Despite the lack ofempirical support game theory can be useful to a security manager be-cause it can help focus attention on the idea that terrorists will change

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strategies in response to improved security Effective security needs toanticipate all possible scenarios and adapt to changing strategies

Insights into the fight against terrorism can come from many differentdisciplines and a security manager must keep an open mind In the fightagainst terrorism simple probability is not sufficient to model a cata-strophic risk that has malicious human intent Security managers shouldseek out expert advice and cooperate with the government and other orga-nizations even rivals to protect against ever changing terrorist threats

REFERENCES

Altman D (October 10 2002) Nobel that bridges economics and psychology NewYork Times Business page 1

Arnold L (June 28 2003) Washington State among winners in race for federal secu-rity funds The Associated Press State and Local Wire Section State and Regional

Black B (April 1 2002) Applying John Nashrsquos game theory to make terrorism insur-ance coverage more available to American business Marketplace Morning ReportCopyright 2002 Minnesota Public Radio

Dubner S J (August 3 2003) The probability that a real-estate agent is cheating youThe New York Time Magazine pg 23-27

Ferguson B (February 24 2002) Playing games with a beautiful mind The Daily SunSection Commentary (Copyright 2002 Knight RidderTribune News Service)

Gass SI (December 2003) Ask the Experts Scientific America Pg 124 (Edited byMatt Collins)

Gately E (March 24 2002) Movie Subject Advanced Game Theory Economic Prin-ciples East Valley Tribune (Mesa Arizona) (Copyright 2002 Knight RidderTri-bune Business News)

Hilsenrath J E (October 10 2002) Nobel winners for economics are new breed WallStreet Journal page 1

If life is but a game why not play by the rules (January 11 2002) Financial Times In-formation Global News Wire Katsuri amp Sons Ltd

London S (March 26 2002) Games or serious business Financial Times (LondonEngland) Section Inside Track Pg 16

Major JA (February 2002) Advanced Techniques for Modeling Terrorism RiskGuy Carpenter amp Company Inc From Web Site wwwguycarpcom accessed onNovember 24 2003

References in Majorrsquos Paperbull Quade E S (1966) Analysis for military Decisions Chicago Rand-McNallybull Woo G (2002) ldquoQuantifying insurance terrorism riskrdquo Risk Management So-

lutions Inc To appear in Alternative Risk Strategies M Lane ed Risk Publica-tions Ltd

Marano L (May 8 2003) Expert Nations must join against terror United Press Inter-national


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Matthews R (February 24 2002) Itrsquos not how you play the game itrsquos whether you ap-ply Nashrsquos theory Sunday Telegraph (London) Pg 33

New Guy Carpenter report addresses challenges of modeling terrorism risk Study usesgame theory to analyze terrorism risk for insurance industry (March 25 2002)Business Wire Inc

Report In principle terror risk can be modeled measures (March 2002) AM BestCompany Inc Best Wire

RMS launches game theory-based terrorism risk model model introduced at seminaron terrorism risk attended by 250 RMS Insurance and reinsurance clients (Septem-ber 18 2002) PR Newswire association Inc Financial News

What is game theory (April 21 2003) The Economic Times of India Coleman amp CoLtd (Global News Wire)

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sub-licensing systematic supply or distribution in any form to anyone isexpressly forbidden Terms amp Conditions of access and use can be found athttpwwwtandfonlinecompageterms-and-conditions

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STUDENT PAPERS


Brian Seymour BA








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CONCLUSION


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REFERENCES
















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STUDENT PAPERS


Brian Seymour BA








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CONCLUSION


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REFERENCES
















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CONCLUSION


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REFERENCES
















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o C

olle

ge]

at 1

643

27

Oct

ober

201

4







Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Student Papers 101

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4








Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 99

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4







Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Student Papers 101

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 99

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4







Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Student Papers 101

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4







Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Student Papers 101

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Student Papers 101

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4









Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






CONCLUSION


Student Papers 103

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4



REFERENCES
















Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4






Student Papers 105

Dow

nloa

ded

by [

Col

orad

o C

olle

ge]

at 1

643

27

Oct

ober

201

4