Self-Containment: Achieving Peace in Anarchic Settings

36 Pages·2014·0.19 MB·English

Self-Containment: Achieving Peace in Anarchic Settings
AntonisAdam∗andPetrosG.Sekeris†
November2014
Abstract
In anarchic settings, potential rivals can be dragged into arms races degenerating in open wars out
ofmutualsuspicion. Weproposeanovelcommitmentdeviceforcontestantstoavoidbotharmingand
fighting.WeassumethattheMilitarydecidesthearmamentlevelsofacountry,whiletheCiviliandecides
whethertoattackarivalcountry. Whenthesedecision-makingbodiesperfectlycommunicate,thedeci-
sionmakersareunabletocrediblycommunicatetotheirfoetheirwillingnessnottoarmandnottoattack,
thusimplyingthatwarensues. Withimperfectinformation,however,peacemayensueascountriescred-
iblysignaltotheirrivalamorepeacefulstancesincecontestantsaremorereluctanttoenterinanarmed
confrontationwithapotentiallyunderstaffedarmy. Usingdataonthe1975-2001period,weprovidesup-
portiveevidencethatincountrieswheretheheadofthestateorthedefenseministeraremilitaryofficers,
and are therefore better informed of their armies’ fighting preparedness, the likelihood of observing an
internationalconflictishigher.
Keywords: Conflict;PrivateInformation;Commitment
JELclassification: D74;D82;F5;H56
Wordcount: 10,989
∗Thispaperhasgreatlyimprovethankstotheexcellentcommentsofourreferees.WearehighlygratefultoFelixVardyandAnasta-
siaLitinafortheirveryhelpfulsuggestions.WealsothankEmmanuelAthanassiou,UgurhanBerkok,VincenzoBove,EricBrousseau,
RaulCaruso,EshienChong,MikhailDrugov,JohndeFiguereido,MichelleGarfinkel,Jean-DenisGaron,CharalambosHristou,Chris-
tosKollias,KaiKonrad,FragoKourandi,AthanassiosPitsoulis,RobertPowellandEmmanuelRaynaudfortheircomments. Antonis
AdamisLecturerattheUniversityofIoannina.Contacte-mail:[email protected]
†PetrosSekerisisPrincipalLecturerattheUniversityofPortsmouth.Contacte-mail:[email protected]
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1 Introduction
Wars produce both victors and losers, and give rise to inefficiencies that affect all contenders. The ineffi-
cienciesmaybedirectsuchashumanlifelossandmaterialdestruction, orindirectwhenittakestheform
ofresourcesdevotedtothepreparationofanarmedconfrontation. Thesetwofeaturesofwarconstitutethe
backboneofthewar’sinefficiencypuzzleexplainingwhyrationalagentsfailtoreachpeacefulsettlements
(Fearon 1995, Powell 2006). Among the several mechanisms that have been identified and that explain
warbetweenrationalagents,theinformationalchannelseemsparticularlyundisputed: leadersholdprivate
information on their military capability which may lead them to mistakenly estimate - and to potentially
over-estimate - their winning odds, thus resulting in undesirable military disputes (Blainley 1988, Fearon
1995,Powell1999,MeirowitzandSartori2008,BaligaandSjo¨stro¨m2012). MeirowitzandSartori(2008)
uncover a fundamental mechanism tying information imperfection to conflict since they demonstrate that
there exist configurations where when both contestants are armed, at least one contestant will want to de-
clarewar. Thisanticipationincentivizesbothopponentstosecretlyarmthusfulfillingtheexpectationofan
armedequilibriumandofwar.Insuchcontexts,moreinformationisdesirablesinceallowingplayerstocom-
municatemaycontributetoreducingthelikelihoodofwar(BaligaandSjo¨stro¨m2004). Inthismanuscript
wereversetheargumentsincewedemonstratethatbetterinformationmayincentivizeplayerstoarmandto
declarewar.
Oneofthebuildingblocksofourtheoryisthewayweconceptualizetheinternalorganizationofgovern-
mentsandthecommunicationamongitsdifferentconstituencies. Thebulkoftheliteratureoninformation
quality in international relations has considered states as unitary actors. Yet, experts in Civil-Military re-
lationsremindusthatthishypothesisisnotalwayssatisfied(Huntington1957,Desch1999,Feaver2003).
Governments have often pursued a separation of powers, with the Military holding private information on
sensitive issues regarding the country’s security (Feaver, 2003). In such instances, a country’s domestic
securityandforeignpolicybecomehighlydependentonthedegreetowhichthedifferentdecision-making
bodiesareabletocommunicate(Huntington1996,Desch1999,Feaver2003).1
Before delving into the consequences of such information asymmetries on foreign policy, it is worth
examining their roots. First, the Civilian-principal and the Military-agent may face agency problems and
have mis-aligned objectives (Feaver 2003, Acemoglu et al. 2010). Communication problems constitute a
1OntherelatedquestionoftheoptimalamountofpowertheCivilianshouldgranttheMilitaryseeBiellingandGarfinkel(1997),
BesleyandRobinson(2010),Acemogluetal.(2010),BoveandNistico`(2014),andLeon(2014).
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secondcause. Jervis(2010),forinstance,exposesthecommunicationproblemsbetweentheUnitedStates’
intelligenceandthecountry’sdecisionmakers. Thismayinturnproducewrongevaluationsofone’sown
capacitytocopewithaninternationalcrisis. AthirdreasonwhyCivilian-Militaryrelationsmaybehurtby
informationimperfectionliesintheCivilian’saccountabilitytothepublicopinion(PageandShapiro1983)
whichtypicallylackstherequiredexpertiseinmilitarymatters(Gelpi2010)andyetinfluencesforeignpol-
icy. Overall,itisreasonabletoexpectallthesefactorstosimultaneouslyimpactthequalityofinformation.
Withthisempiricalrealityinmindwenowexplorethetheoreticalimplicationsofinformationalimper-
fectionsinsidecountriesonthelikelihoodofwar. Thetheorydevelopedinthispaperbuildsontheseminal
contributionofStergiosSkaperdas(1992)whichmodelsconflictasazero-sumgame. Insuchsettingspeace
is never reached because of an underlying arms race logic that constrains both parties to prepare for war
despitetheParetosuperiornatureofaweaponless,andhencepeacefulorder. Ontheonehandaweaponless
enemyconstitutesaperfectprey,thusmakingtheweaponlessequilibriumunrealizable. Ontheotherhand,
armingtodeteranaggressionmakesoneselfincreasinglywillingtousethesegunsifthefoeisexpectedto
be lightly armed. At equilibrium, both contestants end up being armed, and the setting being a zero-sum
game, it is always (weakly) in the interest of one contestant to declare war.2 This mechanism has been
clearlyexplainedbyJervis(1978)whotermedthecountries’tendencytoarmoutofmutualfearthesecurity
dilemma:“[M]anyofthemeansbywhichastatetriestoincreaseitssecuritydecreasethesecurityofothers”
(Jervis,1978: 169).
In this paper, we reverse the arms race logic by introducing in Skaperdas’ (1992) benchmark model a
particular form of information imperfection. We graft on a standard “guns and butter” model information
imperfections inside each country. From an individual viewpoint, reduced communication implies a less
accurate knowledge of one’s own military efficiency. Yet, a disregarded consequence is that the implied
reducedmilitaryefficiencyofaparticularcountrymayyielddesirableequilibriumoutcomessincetheop-
ponentwillhaveincentivestoreducehismilitarizationtherebytriggeringade-escalationspiral. Toclarify
the underlying logic, consider two countries A and B where the Military in each country is in charge of
armamentdecisionswhiletheCiviliandecideswhetherornottoenterinamilitaryconfrontationwiththe
rivalcountry. AssumefurtherthattheMilitarycommunicatestohisCivilianthecountry’sstrikingcapacity
(i.e. amountsofweapons),yetinanimperfectmanner,andthatthisisoccurringinbothcountries. Should
2Innegative-sumgamespeacefuloutcomesmayemergeatequilibrium(GrossmanandKim1995,Jacobsson2009,DeLucaand
Sekeris,2013).Inthispaperweunveiltheself-containmentmechanisminazero-sumgameenvironmentthatotherwiseproduceswar
equilibria.Thismechanismcanstraightforwardlybeextendedtonegative-sumgames.
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the Military in country A build up a powerful army and communicate this information to his Civilian, the
latterneverthelessremainsunsureofitsarmy’sstrikingcapacityandcouldthereforerefrainfromattacking
arivalwhoseexpectedstrengthislowerthanone’sreal(yetunknown)strikingcapacity. Inanticipationof
their respective Civilians’ reaction, both Militaries consequently have incentives to refrain from preparing
forbattle(i.e. fromarming)withpositiveprobability,thusfeedingbackintheCivilians’reluctancetoini-
tiateconflict. Followingthislineofreasoning,theextremecasewherebynoMilitaryarmsandnoCivilian
initiateshostilitiesconstitutesanequilibrium,thoughnottheonlyone. IncontrastthereforetoJervis’secu-
ritydilemma(Jervis1978)andtothearmsraceliterature,informationimperfectionswouldallowcountries
toenterinade-escalationspiral. Thisisthenovelmechanismwepresentinthispaperwhichallowsforthe
emergenceofpeacefuloutcomeswherethebulkofthetheoreticalliteraturepredictswar.
It is noteworthy that we depart from the standard principal-agent approach (Feaver 2003) where the
Civilian-principal’sandtheMilitary-agent’spreferencesdiffer.Thetheorydevelopedinthispaperassumesa
combinationofperfectalignmentofincentivesandofinformationimperfections.Thisassumptionpermitsus
tobetterhighlighttheimplicationsofimperfectinformation,whichwouldbepresentevenifthetwobodies’
preferenceswerenotperfectlyaligned. Imposingamisalignmentofincentiveswouldfurtherreinforceour
results,butwouldequallycastdoubtsonthesourceofthemechanismunderlyingourresults.
Meirowitz and Sartori (2008) equally focus on information imperfections but reach diametrically op-
posed conclusions. The type of information asymmetries in these two papers differ, however, since we
impose that they arise not only between opponents, but equally inside each contesting party. In the peace
equilibria we derive in this model, the probability that parties follow their hawkish strategy (i.e. invest in
weapons)isstrictlylessthanonebecauseofinformationimperfections. HadtheMilitaryandtheCivilian
beenabletoperfectlycommunicateasinMeirowitzandSartori(2008),however,anticipatingthattheoppo-
nentmaybeunarmedwouldincentivizeoneselftopurchasearms(withcertainty)andthereaftertoinitiate
hostilities. Theveryanticipationofthisreactionwouldthereforeruleoutweaponlessequilibria.
The theoretical findings of the paper are the following. War occurs with certainty when two countries
withperfectlyinformeddecision-makersfaceeachother. Ifbothcountriessufferfrominformationimper-
fections,peacecanoccureitherasapurestrategywherebothcountriesareweaponless,orelseasamixed
strategywheretheprobabilityofarmingandoffightingarebothstrictlypositivebutlessthanunity. Allow-
ingforanill-informedcountrytoconfrontaninformedoneyieldsintermediateresults: eithertheinformed
country always finds it optimal to initiate conflict, or else there exists scope for a mixed strategy equilib-
riumproducingpeacewithastrictlypositiveprobability. Thesefindingsimplythatthemoreinformedthe
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country-pairs,themorehawkishthecountriesarelikelytobe,whiledovishbehaviorfollowsfrominforma-
tionimperfections.
Inthefollowingsectionwepresentsomestylizedfactssuggestingthatbetterinformedregimestendto
bemorebelligerent. InSection3weexposethemodelandthetheoreticalfindings. Next,inSection4we
supportourtheorywithempiricalevidenceandinSection5weconfrontourempiricalresultstopotentially
competingtheories. ThelastSectionconcludes.
2 Information quality and bellicosity: stylized facts
Measuringthequalityofinformation
Sinceourpresumptionisthatbetterinformedregimestendtobemorebelligerent,wefirstoughttodevise
areliablewayofmeasuringthequalityofinformation. TheMilitarybeingaprofessionalbody,itpossesses
private information over important issues like tactics and logistics (Fearon, 2003:69). Desch (1999) and
Feaver (2003) emphasize that the ‘Civilian’ fails both in having perfect knowledge of sensitive military
information,andinfullycontrollingthemilitary. Thispointisevenmorerelevantinlightoftheanalysisof
Jervis(2010)whoexposestheproblemsofcommitmentbetweenintelligenceagenciesandtheirrespective
governments.Theexchangeofinformationamongkeypoliticalandmilitarydecisionmakerstypicallytakes
place,however,underaveilofsecrecythatpreventsusfromhavingdirectaccesstosuchdata.Alternatively,
suchdatacouldbeproxiedbycharacteristicsofthedecisionmakersthatfacilitatetheflowofinformationon
anarmy’smilitarypreparednesswhichisacombinationofarmamentslevels,technology,militaryexpertise,
intelligence and so forth. Since military officers are certainly among the better informed regarding their
country’scombatcapacity,itisnotunreasonabletoassumethatwheneveramilitaryofficialparticipatesin
thehighestechelonsofthegovernment-astheheadofthegovernmentorasadefenseminister-theflowof
informationintheregimeishigherthanotherwise.Fortheremainingofthepaperweadoptthisassumption.
Figure1aallowsustoobtainafirstunderstandingofthelinksbetweeninformationqualityinsidearegime
and its bellicosity. On this figure we have plotted for each country the (logarithm of the) average military
expendituresasapercentageofGDPandtheaverageprobabilityofwarovertheperiod1975-2009. Given
thelargenumberofcountriesthatexperiencedzeroconflictsoverthisperiod,wechosenottorepresentthese
on thefigure for presentationreasons. Thetriangles designate militaryregimes (i.e. well informed) while
the diamonds represent non-military regimes (i.e. ill-informed). The figure reveals that on average better
informed regimes tend to be more belligerent, thereby giving a first indication of a possible link between
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figure(1a) figure(1b)
informationqualityandacountry’sbelligerence.
Theseroughstylizedfactsindicateapossibleconnectionbetweeninformationqualityandforeignpolicy.
Itcouldbeargued,however,thatourcategorizationisproblematicbecauseofthepotentiallyhighcorrelation
betweenourmeasureofinformationqualityandthedegreeofdictatorship,eventuallyblurringthepicture.
Nevertheless,thedatarevealthat28%ofcountrieswithpositivepolityIVscoresare‘informed’following
ourdefinition,while35%ofthecountrieswithnegativepolityIVscoresare‘uninformed’. Thiscanpartly
be seen by a visual comparison of Figures 1a and 1b. Figure 1b features the same elements as Figure
1a, and instead of depicting the degree of information we are distinguishing regimes on the basis of how
democratictheyare. Morespecifically, theredcrossesrepresentregimeswithaPolityIVscorebelowthe
worldmedian,andthebluecrossesdesignateregimeswithapolityscoreabovethemedianworldscore. We
observethatthemostbellicosecountriestendtobemoredemocratic. Thisobservationdoesnotcontradict
the democratic peace argument given that the large majority of countries that we have not reported on the
figure because of their peaceful history throughout the period under consideration are equally democratic.
This does, however, hint to characteristics of some democratic regimes making them more bellicose than
others:asmallgroupofdemocraciesseemtobedisproportionallywar-prone,andthebulkof(non-reported)
democracies do not experience wars. The second interesting feature is that no clear pattern between the
degree of information quality and the degree of democracy seems to emerge from a rough comparison of
thesetwographs. Thisnotonlycomfortsusinourchoiceoftheinformationqualitymeasure, butthefact
that the most war-prone democracies are equally better informed countries suggests that the characteristic
polarizingdemocraticregimesintheirbellicositymaywellbetheinformationquality.
Some concrete examples on the non-overlap between our measure of information quality and regime
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typemayhelpconvincethesceptics.KenanEvrenwhobecameChiefofGeneralStaffofTurkeyin1978led
amilitarycoupin1980andinstalledhimselfatthecountry’spresidencywhereheremaineduntil1989. In
July1983,however,EvrenresignedfromtheCommandoftheArmy. DespitethefactthatTurkeywasbeing
led by a former military putschist, democratic reforms, including the organization of free and democratic
electionsfrom1983onwards,enabledthecountrytoobtainaPolityIVscoreof7over1984-1989,ascore
which objectively categorized Turkey among the democratic nations. Another characteristic example of
an ‘informed democracy’ is the case of Israel. Indeed, over the period covered by our sample, several
headsofstate(YitzhakRabin: 1974-1977,BinyaminNetanyahu: 1996-1999and2009-,EhudBarak: 1999-
2001, Ariel Sharon: 2001-2006, Ehud Olmert: 2006-2009), and defence ministers (Ezer Weizman: 1977-
1980,YitzhakRabin:1984-1990and1992-1995,YitzhakMordechai:1996-1999,ShaulMofaz:2002-2006)
have been at some point during or prior to their political career military officials. Nevertheless, Israel has
systematicallybeenattributedsinceitscreationin1948apolityIVscoreof9or10.3
Thestylizedfactspresentedinthissectionseemtosuggestalinkagebetweeninformationqualityina
countryandthelikelihoodofbeinginvolvedinaninternationalconflict. Thenextsectionproposesatheory
explainingthesepreliminaryfindings.
3 The Theory
3.1 TheSetting
Two countries share a territory of total worth R, such that country 1 controls a share λ ∈]0,1[ of it, while
country 2 has property rights over the remaining territory. Each country’s territorial endowment ri ∈ R
constitutestheuniqueinputintheproductionofaconsumableci (i = {1,2}),givenaunitmarginalcostof
production,andintheproductionofarmamentsai. Thesepropertyrightswhichshouldbeseenasthestatus
quopartitionoftheresourcescanbecontestedbyeithersidebygoingtowarandaresuchthatr1 =λRand
r2 = (1−λ)R. In each country, a CivilianCi (i = {1,2}) is in charge of the decision to fight (i.e. declare
war)ortoconcede(i.e. notdeclarewar). Ifwartakesplace,theremaining“pie”atstakeisthereforeequal
toλR−a1+(1−λ)R−a2 =R−a1−a2. Thelikelihoodthatcountryiwinsisthendescribedbyafunction
3Anotherpotentialconcernwithourmeasureofinformationqualityemergesfromtheconstitutionaldesignimposinginmany
countriesthathighlyrankedCivilianofficialsrenegeontheiractiveinvolvementintheMilitary(withoutusuallycompellingtheMilitary
toresignfromtheirpositioninthearmy).Notice,however,thatsuchconstraintsreinforceourinformation-basedexplanationsincethey
filter-outthepotentialforacountry’swar-pronenessbeingtheconsequenceofaCivilianofficialhavingvestedinterestsinthearmy.
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p(ai,a−i)anddependsontheamountsofarmamentsavailableincountry1and2,respectivelydenoteda1and
a2. Thewinnerofthecontestgainscontroloverallthecontestedresources. Thearmamentlevelofcountry
iisdecidedbyitsMilitary,Mi. Giventhatthemarginalcostofarmingismeasuredasanopportunitycostof
foregoneproduction,Mihastorespectitscountry’sbudgetconstraint: ri =ci+ai. Thefunction p(ai,a−i)is
assumedtosatisfythefollowingproperties:
H.1. pi = p(ai,a−i)= f(ai) if ai+a−i >0,with f(0)=0, f(cid:48)(.)>0, f(cid:48)(cid:48)(.)≤0
f(ai)+f(a−i)
(cid:16) (cid:17)
H.2. p1,p2 =(λ,1−λ) if ai+a−i =0
We thus assume that a country’s fitness is decreasingly increasing in the size of its army, while in the
absenceofarmies(a1 =a2 =0),thewaroutcomeisassumedtobethesameasthestatusquo.4 Becauseof
assumptionsH.1. andH.2.,theprobabilityfunctions,andhencethewarpayoffs,experienceadiscontinuity
in (a1,a2) = (0,0). As a consequence, throughout the paper we denote by σi the probability that country
i arms (ai > 0), and (1−σi) therefore designates the probability country i remains weaponless (ai = 0).
Moreover,weallowformixedstrategiesinthefightandconcedeactions,andaccordinglydenotebyπi the
probabilitycountryiattackscountry−i.
Thecountriescandifferalongtheirdegreeofcentralizationwhichisreflectedinthe(exogenous)quality
ofinformationflowingfromthecountry’sMilitarytoitsCivilian. TheMilitarydecidesanarmingstrategy
and then privately communicates to his Civilian his arming strategy (i.e. the opposing country’s actors do
notobservethesignal),buttheflowofinformationisimperfect. Denotingthearmingstrategysetofcountry
i’sMilitarybySi ={si,...si},ifMiplayssi ∈Si,Cireceivesasignalαi = si withprobability(1−(cid:15)). The
1 n k k
(cid:15) probabilityofmistakensignalsisuniformlydistributedovertheremainingsetofarmingstrategiesSi\si.5
k
Notice that to keep the model meaningful we restrict (cid:15) to the interval [0;1[.6 Throughout the analysis we
imposethatacountry’sCivilianandMilitaryderivethesameutility.7
Givenourmodellingstrategy,anaturalquestioniswhethertheassumedinformationimperfectionsare
compatible with the players’ incentives to communicate each other information: is it not in the interest
of the Military to perfectly communicate to its Civilian the country’s armament level for the latter not to
4Alltheresultsremainqualitativelytrueforanyp(0,0)∈]0,1[.
5WefollowBagwell’s(1995)wayofintroducinginformationimperfectioninthestrategiesoftheplayersratherthanintheiractions
asisusuallyassumed.
6Allowing(cid:15)toequalunitywouldcreatesituationswhere‘verybad’signals(i.e.(cid:15)=1)providetheplayersasmuchinformationas
‘verygood’signals((cid:15)=0).Wedismisstheseunrealisticcasesthatwouldbringnoadditionalinsightstotheanalysis.
7Resultsarerobusttorelaxingthisassumption.
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takewrongdecisionsoutofignorance? Whilewearemerelyassuminginthepresentversionofthepaper
that information imperfections subdue for reasons out of the players’ control, our findings suggest that
both players could be better-off under imperfect information, and that both players could therefore have
incentives to commit not to unilaterally improve the flow of information from their own Military to their
Civiliandecisionbody. Intheon-lineappendix,weshowusingalimitingcase(i.e. perfect-symmetry)asan
illustrativeexamplethatamongthemultipleequilibriaofthegamethatemerge,thereexistsanequilibrium
wheresomedegreeofimperfectinformationisincentivecompatibleprovidedacommitmenttechnologyis
available.
Using superscript w to designate the war outcome, and respectively denoting the utility of decision-
makersincountries1and2,byUandV,itfollowsthatcountry1’sdecisionmakerutilityunderwarisgiven
bythefollowingexpression:
(cid:16) (cid:17)
Uw = p(a1,a2) R−a1−a2 (1)
Usingthesuperscriptw¯ todesignatethepeaceoutcome,wehave:
Uw¯ =λR−a1 (2)
The timing of the game is sequential. In the first stage of the game, the agents responsible for the
resourceallocation-theMilitary-decidetheamountofgunstopurchaseandtheamountofconsumables
toproduce. Inthesecondstage,theagentsresponsibleofthewardecisions-theCivilians-simultaneously
decidewhethertoattacktheirfoeornot. IfeitherCivilianplaysfightwarensues. Wesolveforthegame’s
sequentialNashEquilibria. Wesolvethegamebybackwardinduction.
3.2 Modelwithfullinformation(cid:15)i = 0, i = {1,2}
Assume first no information imperfection. Given the timing of the game, we first derive the Civilians’
optimaldecisionsforanycombinationsofarmamentlevels.
Thedecisionofgoingtowar
Sinceinformationisperfect((cid:15) =0),theCiviliansperfectlyobservetheirowncountry’sarmamentlevels,
andtheyarebothawaretheiropponentsdosoaswell. Hence,ifCivilianC1 observesa1 =0⇔σ1 =0,his
expectedutilityofplayingfightequals:
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Uf(a1,a2)|a1=0 =σ2Uw(0,a2)+(1−σ2)Uw¯(0,0) (3)
wherethefirsttermstandsforthepayoffofCivilian1whencountry2declareswar,whilethesecondterm
isCivilian1’spayoffifcountry2doesnotdeclarewar,i.e. underpeace.
Notice that since Civilian C1 does not observe the signal sent by M2 to C2, C1 ought to rely on his
expectationsastowhether M2 hasarmedornot. Tolightennotation, weareslightlyabusingnotationand
wetakeσ2todesignatetheexpectationofC1thatM2hasarmed.ItisalsonoteworthythatifneitherMilitary
hasarmed,sothata1 = a2 = 0,wehavebyAssumption2thattheexpectedoutcomeisthesameasunder
peace.
Playinginsteadconcedeyields:
(cid:16) (cid:17)
Uc(a1,a2)|a1=0 =π2Uf(a1,a2)|a1=0+(1−π2) σ2Uw¯(0,a2)+(1−σ2)Uw¯(0,0) (4)
whereuf(a1,a2)|a1=0isgivenby(3)andgetsrealizedifCivilian2decidestofight.
Combiningtheseexpressionsallowsustoobtain:
Uc(a1,a2)|a1=0 >Uf(a1,a2)|a1=0 ⇔Uw¯(0,α2)>Uw(0,α2)=0 (5)
wherethesecondstrictinequalityfollowsdirectlyfromUw¯(0,a2)=λR>0. Hence,ifai =0,Cialways
concedes.
IfC1 receivesasignala1 > 0 ⇔ σ1 = 1,wecanagaincomputehisutilitywhenheeitherconcedesor
fights. Ifheplaysconcedehisexpectedutilityequals:
(cid:16) (cid:17)
Uc(a1,a2)| =σ2π2Uw(a1,a2)+σ2 1−π2 Uw¯(a1,a2)+(1−σ2)Uw¯(a1,0) (6)
a1>0
TheexpectedutilityofCivilian1isnowcomposedofthreeterms,respectivelystandingfor(i)Country
2 being armed and declaring war, (ii) Country 2 being armed but refraining from declaring war, and (iii)
Country2notbeingarmedandthereforenotdeclaringwarasdemonstratedabove,inwhichcasethepayoff
ofCivilian1isthepeacepayoff.
Whenplayingfightinstead,theutilityofCivilian1isgivenby:
Uf(a1,a2)| =σ2Uw(a1,a2)+(1−σ2)Uw(a1,0) (7)
a1>0
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