253

Intra－industry　Trade　and　International　Technology　Conlpetition

塩　　澤　　恵　　理

　　　　Eri　Shiozawa

Introd〔」ction

　　In　traditional　trade　theory，　one　country　buys　goods　from　another　and　sells　other

goods　to　another　country　according　to　the　rules　of　comparative　advantage．　Here

the　goods　imported　and　exported　are　different　products；thus，　there　is　no　room　for

competition　between　the　traded　goods．　This　simple　theory　of　comparative　advantage

originally　developed　by　David　Ricardo，1ater　refined　by　Hecksher　and　Ohlin　with　the

final　touch　by　Paul　Samuelson，　envisions　trade　situations　in　a　static　context．

Therefore，　the　countries　and　commodities　concerned　are　by　no　means　competitive．

Instead，　countries　engaged　in　trade　are　cooperative　and　achieve　the　so　called　貿gains

from　trade”．　As　an　example，　Japan　imports　oil　from　Saudi　Arabia　in　exchange　for

Sony’s　Walkman．　Japan　needs　oil　and　Saudi　Arabia　needs　electric　appliances．　By

Japan　specializing　in　high－tech　products　while　Saudi　Arabia　specializes　in　oil

production，　both　countries　get　what　they　need　in　large　quantities．

　　Two　countries　will　naturally　cooperate，　because　that　is　the　only　way　that　gains

from　trade　will　result．　Here　the　essential　point　in　traditional　trade　theory　is　that

both　countries’comparative　advantages　do　not　change　and　that　two　countries　are

willing　to　cooperate．　This　may　be　called　trade　with　static　and　cooperative　game．

However，　in　actual　situations，　history　has　proved　that　in　the　long－run，　a　country’s

comparative　advantage　can　be　and　should　be　improved．　This　is　known　as更ぞ

?モ盾獅盾高奄メ@development”．

254　　　　　　　　　　『明大商学論叢』第82巻第1号　　　　　　　　　　（254）

　　Japan　fifty　years　ago　was　a　poor　country　specializing　in　low－tech　toy

manufacturing　while　the　U．S．　fifty　years　ago． @was　already　engaged　in　the　advanced

manufacturing　industry．　Japan　sold　toys　in　exchange　for　advanced　machinery　made

in　the　U，S．；since　then，　Japan　achieved　economic　development　and　is　now　exporting

high－tech　products　to　the　U．S．　in　exchange　for　agricultural　products．　This　is　the

definite　trend　that　we　observe　now．　In　this　case，　the　comparative　advantage

reverses　itself　in　favor　of　Japan；but　still　goods　traded　between　the　U．S．　and　Japan

are　different　products．　However，　in　the　course　of　Japan’s　economic　development，

there　is　another　trend　which　is　disturbing　to　some　economists　and　politicians．　Japan

has　developed　to　the　stage　that　she　can　produce　the　same　products　which　the　U．S．

has　been　proud　of；that　is，　Japan　can　compete　with　the　U．S．　in　many　fields

including　automobile　and　other　high－tech　products　such　as　semi－conductors．

　　America　was　the　champion　of　auto　manufacturing，　but　Japan　may　claim

superiority　in　the　same　auto　industry　thereby　creating　trade　friction．　This　situation

has　never　been　explained　by　static　trade　theory．　It　was　only　over　a　decade　ago　　　　　　　　　　　　　　　　（1）

when　Paul　Krugman　of　the　Massachusetts　Institute　of　Technology　saw　this　situation

as　different　from　the　traditional　one．　This　is　trade　within　the　same　industry　known

as　intra－industry　trade：　trade　actually　occurs　in　the　same　industry　between

industrial　countries　that　have　relatively　similar　factor　endowments　or　si’milar　factor

intensity．　However，　what　Krugman　did　not　do　is　construct　a　model　which　creates

intra－industry　trade　as　a　natural　consequence．　Earlier　papers　attempted　to　do　this　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　（2）

by　introducing　the　product　cycle　theory　by　Raymond　Vernon　and　much　earlier　by　　　　　　　　　　　　　　　（3｝

Kaname　Akamatsu．　Akamatsu’s　geese　flying　model　in　the　1930s　already　assumed

that　the　very　concept　of　comparative　advantage　needed　to　be　revised．

　　If　one　accepts　that　trade　may　be　based　not　only　on　static　comparative　advantage，

but　also　on　dynalnic　comparative　advantage　of　intra－industry　trade，　then　one　must

also　accept　possibilities　of　friction　and　competition　among　trading　partners．　This　is

an　entirely　different　situation　from　the　case　where　trade　will　automatically　benefit

the　countries　involved　in　trade．11n　fact，　trade　may　hurt　the　partner　relationship．　If

Japan　exports　too　many　cars　to　the　U．S．　while　shutting　out　American　cars　from

Japan，　America　may　accuse　Japan　of　exercising　unfair　trade　practices．

　（1）E．Helpman　and　P．　Krugman，　Market　Structure　and勘吻gηTrade，（Cambridge，

　　　Mass．：The　MIT　Press，1985）．

　（2）Raymond　Vernon，　tclnternational　Investment　and　International　Trade　in　the　Product

　　　Cycle，”Quarterlyノ磁甥α10f　Economics，（1969，　May），190－207．

　（3）Kaname　Akamatsu，　Sekai　Keizai　Ron，（Tokyo：Kunimoto　Shobo，1965），165－181．

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　　1n　this　paper　we　attempt　to　analyze　a　simple　model　of　trade　competition　when

two　countries　engage　in　intra－industry　trade　utilizing　the　analysis　of　Ryuzo　Sato’s　　　（4）

work，ヒThe　Technology　Game　and　Dynamic　Comparative　Advantage：An　Application

to　U．S．－Japan　Competition”．　Two　Oountries　try　to　change　their　comparative

advantage　in　the　same　sector　by　investing　in　research　and　development（R＆D）

activities．　Japan’s　industrial　policy　is　known　to　have　contributed　to　the　postwar

success　in　catching　up　to　the　U．S．　in　auto　and　other　high－tech　industries．

Following　Sato’s　work，　we　analyze　the　model　which　incorporates　a　non－cooperatlve

dynamic　game　since　trade　has　two　faces；cooperative　and　bonfronting．

THE　MODEL　　We　will　consider　an　abstract　model　in　which　intra－industry　trade　takes　place　for　a

homogeneous　commodity　Y　which　two　countries　produce’to　sell　in　the　world

market．　The　two　countries　involved　may　be　identified　as　Country　A　and　Country

B．　（Country　A　may　be　the　U，S．　and　B，　Japan．）　Country　A　and　Country　B　use

く喝 ≠撃高盾唐煤hidentical　technology　to　produce　commodity　Y，　say，　automobiles．　The　world

market　consists　of　an　aggregation　of　all　the　markets　in　the　world　including

American，　Japanese，　European，　Latin　Amerian　and　Asian　markets．　Japanese　cars

may　be　exported　to　these　foreign　markets，　while　American　cars　may　be　imported

by　these　markets．　Therefore，　trade　will　take　place　in　automobile　exports　and

imports－－intra－industry　trade　in　automobile．　For　simplicity，　we　will　first　consider　a

two－country　mode1，　which　implies　that　Europe　and　other　Asian　countries　do　not

produce　cars　and／or　do　not　engage　in　automobile　trade．

Stage　l

Technology　is更璽almost”identical　in　that　Country　A　is　the　innovator　while　Country　B

is　the　follower．　With　appropriate　investment，　Country　A　develops　and　innovates　the

technology　necessary　to　produce　commodity　Y．　Country　A　sells　Y　in　the　world

market，　temporarily　catching　the　position　of　monopolist　and　making　abnormal　short－

run　profit．　However，　this　situation　does　not　last　long，　because　entrepreneurs　in

Country　B　see　the　opportunity　to　produce　a　similar　product　to　Y．　What

entrepren6urs　in　Country　B　do　next　is　to　import　the　technology　from　Country　A　by

paying　a　certain　fraction　of　the　development　cost．　In　many　cases，　Country　B　must

pay　patent　fees　to　Country　A．　The　amount　of　the　total　cost　paid　depends　on　the

（4）Ryuzo　Sato，ヒ曜The　Technology　Game　and　Dynamic　Comparative　Advantage：An

　ApPlication　to　U．S．－Japan　Competition，”in　lnternational　Co〃zpetitivene∬，　eds．　M．

　Spence　and　H．　Hazard（NY：BaUinger　Publishing，1988），373－98．

256　　　　　　　　　　『明大商学論叢』第82巻第1号　　　　　　　　　　（256）

situation　where　entrepreneurs　in　Country　B　find　it　difficult　to　produce　cofnmodity　Y

without　access　to　the　technology．　It　also　depends　on　how　easily　the　technology　can

be　imitated　by　Country　B．　Above　all，　it　depends　on　how　entrepreneurs　in　Country

Blook　at　future　profit　conditions．．　More　than　a　decade　ago，　two　Japanese

electronics　companies　were　caught　by　the　U．S．　legal　authority　for　suspicion　of

stealing　a　certain　technology　from　their　U．S．　counterpart．　In　this　case，　the　amount

they　paid　for　acquiring　the　information　was　minimal　although　the　social　and　legal

costs　dealing　with　the　scandal　may　have　been　enormous．

In　Inore　fair　negotiation，　Country　A　and　Country　B　may　share　the　cost　of

developing　the　original　technology　by　equal　amounts．　The　recent　agreement

between　the　U．S．　and　Japan　on　a　certain　aspect　of　space　exploration　falls　into　this

category．

Stage　ll

The　second　stage　of　negotiations　or　the　second　stage　of　thiS　game　strategy　is

concerned　with　the　amount　of　technology　information　that　Country　A　is　willing　to

give　Country　B　in　exchange　for　fees　Country　B　pays　to　Couhtry　A．　As　Country　A

is　a　sole　owner　of　that　information　of　new　technology，　it　tries　to　release　the

minimum　amount　to　Country　B．　For　example，　if　General　Motors（GM）happens　to

develop　a　new　technology　on　automobile　manufacturing，　it　attempts　to　give　away　as

little　information　as　possible　to　Tgyota　even　after　Toyota　pays　a　certain　amount　of

fees　to　GM．　It　is　not　illegal　or　immoral　on　the　side　of　GM　for　doing　this；it　is

simply　trying　to　minirnize　cost，　In　fact　this　is　the　power　of　the　monopolist　in　the

technology　development．

　　The　next　aspect　of　this　dynamic　game　is　related　to　the　fact　that　Country　B’s

technology　is　almost　identical　to　that　of　Country　A．　That　portion　of　information

that　Country　B　acquires　from　Country　A　is　identica1，　but　the　remaining　portion

must　be　created　by　B’s　own　efforts；that　is　to　say，　the　basic　information　of

automobile　production　is　the　same　in　both　countries．　Country　A　has　its　own　unique

way　of　using　that　information　while　Country　B　also　has　its　own　method　of　utilizing

that　information．　This　distinction　is　often　referred　to　as　uniqueness　of　applied

technology。

　For　example，　although　the　basic　information　on　automobile　manufacturing　is　the

same　in　the　two　countries，　the　actual　method　and　strategy　of　production　may　be

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very　different．　The　so　called　American　management　practice　vs．　Japanese　system

in　producing　cars　may　be　very　different．　Toyota　may　use　the　so　called　t’Kanban　　　　　　　（5｝

Hoshiki”（or　just－in－time　method）while　GM　may　use　the　traditional　optimal　　　　　　　　　　　　　　（6）

inventory　method．　The　question　is　how　to　quantify　these　qualitative　differences　in

rnanagement　systems．　In　a　purely　theoretical　model，　it　is　advisable　to　use　some

quantitative　index　to　express　differences　in　the　managelnent　systems．　Here　we

would　simply　differenciate　the　two　approaches　by　the　effectivess　of　management；

that　is，　the　cost　differences　or　the　productivity　differences．　It　does　not　matter

whether　the　Japanese　management　practice　uses　the　so　called　t｛cho－rei”（or　morning

greeting　ceremony）or　the　three　o’clock　exercise　or　karaoke　party　after　five．．　The

point　is　whether　Toyota’s　overall　productivity　is　higher，　equal　to　or　lower　than　that

of　GM．　Therefore，　we　will　ignore　all　the　qualitative　aspects　but　compare． Dsimply

the　productivity　differences．

Let　us　summarize　below　what　we　have　assumed：

1．　Country　A　is　the　innovator　of　the　technology　to　produce　commodity　Y．

II．　Country　B　imports　that　technology　in　order　to　produce　a　product　identical　to

commodity　Y．

III．　Country　B　pays　a　certain　amount　of　fees　to　Country　A　for　acquiring　the

information　to　produce　commodity　Y．

IV．　Each　country　has　its　own　management　strategy　dealing　with　the　applied　aspect

of　technology　management．　The　difference　may　be　quantitatively　measured　by　cost

effectiveness　or　productivity　difference．

STRA丁EGY

　　We　now　consider　how　two　countries　adopt　different　strategies　to　coordinate　all

aspects　of　production，　exportation　and　profit　maximization．　First，　two　countries

must　agree　on　what　type　of　strategy　to　adopt．　Here　it　is　assumed　that　the

technology　game　is　a　Cournot－Nash　differential　game　．　There　are　two　well　known　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　⑦

strategies：open　loop　and　closed　loop　feedback　strategies．　An　economic

interpretation　of　the　open　loop　strategy　is　very　easy；that　is，　once　two　parties　make

adecision，　they　will　never　change　the　time　path　so　that　they　follow　the　fixed　routes

（5）Michael　Cusumano，　The／4加η6sθAutomobile　Industry（Cambridge，　MA：The　Council

　　on　East　Asian　Studies　at　Harvard　University，1985），265．

（6）　Ibid．，270，　281．

（7）　T．Basar　and　G．J．　Olsder，　Dynamic　Noncool）erative　Game　Theo　ry．（London：The

　　Academic　Press，1992．2nd　edition，1995）．

258． @　　　　　　　　　『明大商学論叢』第82巻第1号　　　　　　　　　　（258）

to　the　end．　Therefore，　open　一　loop　strategies　are　functions　of　calendar　time　alone．

In　the　budget　process　as　an　illustration，　this　strategy　is　known　as　an　inflexible

system．　Once　a　decision　is　made，　there　is　no　room　for　adjustment　and　there　is　no

room　for　change　of　path　regardless　of　whether　economic　environrnents　have

changed．

　　The　closed　loop　feedback　strategy　is　a　more　f．lexible　one　because　changes　in

economic　environment　force　the　players　to　adopt　different　paths．　In　other　words，

the　strategy　they　adopt　is　determined　by　the　state　of　the　environment。　In　technical

terminology，　environment　is　the　state　variable；thus，　the　closed　loop　feedback

system　requires　strategy（or　the　control　variable）to　depend　on　the　state　variables　at

each　moment．　This　strategy　is　certainly　much　more　flexible　and　in　the　budget

process　it　is　known　as　a　flexible　budget．　If　the　players　can　condition　their

strategies　on　other　variables　in　addition　to　calendar　time，　they　may　not　want　to　use

open－loop　strategies　in　order　to　react　to　exogenous　moves　by　nature　and／or　mixed

strategies　by　rivals，　etc，；thus，　players　can　respond　to　their　rivals’actions　at　each

period．

　　We　now　discuss　the　objective　function　of　this　dynamic　game．　The　sole　purpose　of

each　country’s　entrepreneurs　is　the　maximization　of　Iong－run　profit．　Therefore，　the

criterion　that　we　use　to　judge　the　outcome　of　the　game　should　be　profit　itself．

But，　since　the　objective　of　the　firm　is　the　functional　rather　than　the　function，　it　is

almost　impossible　to　compare　two　functionals　in　a　dynamic　game．　In　this　case，　the

integral　of　each　year’s　profit　i．e．　the　long－run　profit　from　period　t　zero　to　infinity

is　hard　to　evaluate．　Therefore，　it　is　much　easier　to　use　the　market　share　rather

than　profit　itself　for　comparison．　The　market　share　is　nothing　but　output　itself．

We　will　use　output，　Y　as　the　criterion　of　win　and　loss　of　the　game．　For　instance，

if　Country　A’s　output　Y　is　greater　than　Country　B’s　Y，　we　say　that　Country　A　won

the　game；or　that　Country　B　lost　the　game．　When　output　produced　by　each　country

is　exactly　the　same，　we　say　that　the　game　is　tied．　We　have　to　warn　here　that　we

are　going　to　exclude　two　corner　solutions．　The　first　one　is　the　case　where　Country

Amonopolizes　the　output；that　is，　Country　B’s　output　is　zero．　The　second　corner

solution　case　is　where　Country　B　monopolizes　the　market；that　is，　Country　A’s

output　is　zero．　We　must　exclude　these　cases　because　game　will　not　take　place　under

these　extreme　points．　In　passing，　we　may　say　that　if　Country　A’s　market　share　is

（259）　　　　　　　Intra－industry　Trade　and　International　Technology　Competition　　　　　　　　259

90％rather　than　60％，　Country　A　is　winning　big　and　vice　versa．

lNTERTEMPORAL　PATH　OR　STEADY　STATE

　　Let　us　assume　that　two　countries　have　agreed　to　play　the　game　under　either　open

or　closed　loop　conditions．　Given　the　initial　conditions，　two　players　start

implementing　their　control　variables　in　investment　and　research　to　improve

productivity　and　output　in　order　to　maximize　the　market　share．　What　happens

nextP　That　depends　on　the　inter－temporal　paths．　Two　players　usually　follow　the　so

called　turnpike　path　in　order　to　reach　the　equilibrium　point　or　the　steady　state．　It

is　known　that　there　exists　the　steady　state　where　two　parties　no　longer　want　to

move　away　from　it．　Technically，　we　must　assume　nice　concavity　conditions　on　each

Hamiltonian　function．　It　is　usually　very　difficult　or　almost　impossible　to　describe

the　inter－temporal　path　mathematically　under　this　type　of　differential　game．

Therefore，　we　may　be　happy　to　study　only　the　characteristics　of　the　steady　state　　（8｝

path．

RESULTS

　　Without　becoming　technically　involved，　we　may　analyze　the　economic　implication

of　this　game．

Case　I．

The　simplest　case　is　equal　payment　of　development　cost；that　is，　Country　A　and

Country　B　share　the　equal　amount　of　development　cost　of　theltechnology．　In

addition，　Country　A　gives　100％technology　information　or　full　information．

Furthermore，　Country　A’s　productivity　is　exactly　the　same　as　that　of　Country　B’s．

Under　these　conditions，　the　game　result　is　predictable．　That　is　to　say，　Country　A’s

market　share　is　exactly．identical　to　that　of　Country　B’s（50％vs．50％）。Here，

exports　and　imports　exactly　balance　out．　There　is　no　unfairness　and　there　will　be

no　trade　friction．　The　trade　system　and　game　will　continue　forever．　This　result

apPlies　not　only　to　the　open　but　also　to　the　closed　strategy．

Case　II．

Now　assume　that　even　though　Country　B　pays　development　fees　of　exactly　one　half

to　Country　A，　Country　A　has　the　power　to　exercise　information　control　over　the

technology　on　Country　B．　For　example，　Country　A　gives　away　only　80％of

technology　information　to　Country　B．　What　can　Country　B　do　to　play　the　game～

The　only　solution　for　Country　B　is　to　make　an　extra　effort　to　raise　its　productivity．

（8）Sato　solves　the　technology　game　under　specific　assumptions　in　his　mathematical

　appendix，393．

260　　　　　　　　　　　　　『明大商学論叢』第82巻第1号　　　　　　　　　　　　　（260）

If　Country　B　is　successful，　then　they　can　match　Country　A　in　the　final　outcome．

In　other　words，　provided　that　Country　B　can　substitute　higher　productivity　for　the

lack　of　information，　Country　B　can　cQmpete　with　Country　A　in　the　world　market．

If　productivity　of　Country　B　compensates　for　the　lack　of　information，　there　is　a

possibility　that　Country　B’s　market　share　niay　even　exceed　that　of　Country　A．

Case　III．

If　Country　A　further　reduces　the　defusion　of　technology　information　to　Country　B，

it　is　increasingly　difficult　for　Country　B　to　compensate　this　loss　by　productivity

increase；this　is　due　to　the　law　of　diminishing　returns．　There　is　an　obvious

advantage　for　Country　A　because　it　monopolizes　technology　information．　Is　this

fair？　Country　B　has　paid　one　half　of　the　development　cost，　but　has　received　less

than　full　information．　Country　B． @has　had　an　expectation　of　receiving　full

information　when　the　payment　was　made．　Therefore，　this　is　the　case　of

expectation　unfulfilled．　This　situation　always　happens　when　game　is　played　in　two

stages，　and　nothing　can　be　done．　The　overall　result　shows　that　when　technology

competition　takes　place，　it　is　not　only　the　productivity　difference　that　makes　the

market　share　larger，　but　also　the　degree　of　substitution　between　the　diffusion　of

technology　information　and　productivity　of　manufacturing．

　　Toyota　had　to　work　harder　and　develop　a　method　of”Kanban　Hoshiki”，　because

Toyota　was　originally　the　follower　in　the　auto　industry．　GM　and　other　American’

auto　makers　had　the　advantage　of　full　utilization　of　the　technology．　The　only　thing

Toyota　and　other　Japanese　car　makers　could　do　was　to　depend　on　an　alternative

method　of　raising　productivity．　This　model　clearly　shows　this　type　of　structural

characteristics　faced　by　late　comers　in　the　market．

COMPARISON　OF　DIFFERENT　STRATEGIES

　　We　have　indicated　that　under　the　open　loop　strategy，　optimal　paths　are　Iess

flexible　than　the　case　under　the　closed　loop　strategy．　In　other　words，　the　steady

state　position　under　the　open　loop　strategy　may　be　quite　far　from　the　steady　state

under　the　closed　loop．　There　is　no　reason　to　believe　that　the　two　steady　state

positions　coincide．　In　fact　in　many　cases，　the　closed　loop　steady　state　gives　more

realistic　value　simply　because　the　inter－temporal　path　can　be　adjusted　to　a　more

realistic　environment　or　state　variable．

　Aparadox　may　also　exist　under　the　closed　loop　strategy．　For　example，　even　if

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Country　A　restricts　the　diffusion　of　technology　informaton　to　Country　B，　say　a

20％restriction，　Country　B　may　not　lose　the　competition；or　in　an　extrerne　case，

Country　B’s　market　share　may　improve－－aparadox．　If　this　is　the　case，　Country　A

might　accuse　Country　B　of　unfair　practice　because　this　situatibn　does　not　coincide

with　common　sense．　The　more　Country　A　restricts　information，　the　more　share

Country　B　gets　out　of　from　this　game．

　There　may　be　possible　explanations　for　this　type　of　paradox．　First，　Country　A

has　two　control　variables　to　deal　with，　one　in　developing　the　original（basic）

technology　and　the　other．in　managing　actual（applied）technology　competition．　On

the　other　hand，　Country　B　ha呂only　one　control　variable　of　managing　actual

technology　to　worry　about．　Therefore，　the　closed　loop　strategy　puts　an　extra

burden　on　Country　A．　In　Sato’s　model，　he　points　out　that　an　asymmetry　exists　in

the　Hamiltonian　functions　as　shown　in　his　mathematical　appendix。　Second，　there　is

asunken　cost　in　developing　the　original　technology　by　Country　A．　Country　A　must

have　invested　a　larger　proportion　of　resources　even　before　they　started　the　current

technology　development．　To　develop　automoりile　technology，　many　researchers　must

have　invested　their　time　and　money　before　they　finally　succeeded　in　the　actual

manufacturing；but　the　question　is　who　pays　for　this　type　of　past　investment．

Country　B　is　not　expected　to　pay　for　the　past　investment　cost，　only　the　current

cost．

　An　extreme　case　may　be　the　importation　of　technology　from　the　U．S．　by　an

agrarian　country，　say　a　country　in　Africa．　The　U．S．　has　invested　a　large　sum　of

money　for　the　last　200　years　in　general　technology　developrnent　while　a　country　in

Africa　by　comparison　basically　has　not　invested　in　manufacturing　technology．　If

suddenly　an　African　country　wants　to　import　the　technology　to　produce　the

homogeneous　product　Y，　it　should　pay　the　U．S．　more　than　one　half　of　the　current

investment　cost．　However　in　actuality，　this　is　usually　not　required．　In　the　closed

loop　strategy，　this　difference　may　create　the　existence　of　a　paradox．

CONCLUDING　REMARKS

　　We　have　seen　how　intra－industry　trade　in　a　certain　industry（automobile

manufacturing）may　be　a　factor　that　creates　trade　friction　between　nations（Japan

and　the　U．S．）；this　is　the　result　of　international　competitiveness　in　the　same

industry　which　is　a　departure　from　the　orthodox　way　of　explaining　trade　as　a

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example，　even　if　Country　A　restricts　the　diffusion　of　technology　information（say　by

20％）to　Country　B，　Country　B　may　not　lose　theとompetition，　but　might　on　the

contrary　achieve　improvement　in　overall　rnarket　share．　This　is　a　theoretical

possibility　and　to　Country　A，　it　will　seem　that　Country　B　is　practicing　unfair

competition．　There　may　be　two　reasons　for　this　paradox：First，　with　the　closed

loop　strategy，　an　extra　burden　is　put　on　Country　A　since　there　are　two　control

variables　to　worry　about；that　is，　Country　A　must　worry　about　developing　the

original　technology　and　then　managing　actual　technology　competition．　Whereas，

Country　B　has　to　deal　with　only　one　control　variable　of　managing　actual

technology．　Second，　for　Country　A，　there　is　a　sunken　cost　in　developing　the

original　technology．　We　cah　assume　that　Country　A／must　have　greatly　invested　in　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　ノコ

resources　even　before　starting　the　development　of　t1免technology．　Country　B　is　not

expected　to　pay　for　the　past　investment　cost，　only　the　current　cost．　Therefore，

this　analysis　raises　two　policy　issues．　One　having　to　do　with　international

cooperation，　the　other　with　the　development　of　innovative　technology　in　Country　B．

Innovative　technologies　are　usually　considered　to　be　public　goods；　thus，　the　question

is　how　can　control　be　managed．．This　becomes　a　possible　disputing　point　among

countrles．

　　There　may　be　a　number　of　applications　of　the　model　to　empirical　data．　Sato

applies　the　model　in　order　to　study　the　relationship　between　the　market　share　and

productivity　of　the　Japanese　auto　industry　in　the　U．S．　market．　Sato　shows　how

some　of　the　more　general　conclusions　of　the　model　can　be　tested．　It　is　widely

believed　that　Japan　gained　a　competitive　advantage　in　the　world　automobile　market

during　the　1970s　by　introducing　efficient　process　innovation；and　he　illustrates　the

relevancy　of　the　model　by　comparing　the　actual　trend　of　Japan’s　share　in　the

automobile　market　with　the　productivity　trend　of　Japanese　applied　technology．　Sato

points　out　that　Japan　achieved　comparative　equality　with　that　of　the　U，S．　by　1979

and　gained　comparative　advantage　by　nearly　30％in　1981；therefore，　a　clear

association　between　the　increase　of　Japan’s　share　and　the　rise　of　its　relative

efficiency　could　be　seen．

FURTHER　EXTENSIONS

　　The　above　is　certainly　not　the　full　application　of　the　differential　game．　In　fact，

we　know　no　method　of　such　an　application　as　the　model　involves　the　differential

262　　　　　　　　　　　　　『明大商学論叢』第82巻第1号　　　　　　　　　　　　　（262）

consequence　of　comparative　advantage　among　different　industries　as　analyzed　by

Ricardo　and　his　successors．　Whether　it　is　a　result　of　economic　development　in

which　a　country’s　comparative　advantage　improves　through　research　and

development，　or　simply　the　result　of　product　cycles，　in　the　case　of　intra－industry

tradei　trade　may　hurt　the　country（ies）involved．　This　is　clearly　different　from

static　traditional　theory　in　which　there　is　cooperation　and／or　gains　from　trade．

Therefore，　in　the　analysis　of　this　dynamic　intra－industry　trade　theory，　win　or　loss

（measured　by　market　share）of　the｛｛trading　game”becomes　a　crucial　point．

　We　have　described　a　game－theoretic　model　of　international　technology　competition

following　Sato’s　original　model．　Country　A（the　U．S．）which　is　a　technologically

mature　country　pursuing　in　both　basic　research　and　development　and　applied

technology，　competes　in　the　world　market　with　Country　B（Japan），which

specializes　in　applied　technology．　The　model　assumes　that　the　technologically　mature

country　has　a　dynamic　comparative　advantage　to　the　extent　that　it　can　control　the

diffusion　of　information　related　to　the　basic　technology．　Meanwhile，　the

technologically　less　mature　country　has　a　comparative　advantage　in　applied

technology　provided　that　the　flow　of　basic　information　is　sufficient．

　The　outcomes　of　the　game（Cournot－Nash　dynamic　game）depend　on　the　types　of

strategies　that　the　two　countries　employ．　In　both　the　open　and　closed　loop

strategy，　as　long　there　is　equal　payment　of　development　cost　of　the　technology

between　the　two　countries；and　Country　A　gives　100％technology　information（full

information）；and　the　productivity　of　the　two　countries　is　exactly　the　same，　the　two

countries’share　will　be　50％and　50％．　Exports　and　imports、will　exactly　balance

out；there　is　no　unfairness　and　no　trade　friction．

　　If　they　adopt　the　open　loop　strategy　and　Country　B　receives　less　than　full

information　of　the　basic　technology　from　Country　A，　then　the　Inarket　share　will

depend　on　the　productivity　difference；that　is，　how　can　Country　B　substitute　higher

productivity　for　the　lack　of　information　resulting　from　export　control　of　the

technology　by　Country　A．　In　addition　to　the　productivity　difference，　the　degree　of

substitution　between　the　diffusion　of　technology　information　and　productivity　of

manufacturing　influence　the　market　share．

　　Under　the　closed　loop　strategy，　in　which　the　values　may　be　more　feasible　since

adjustment　to　a　more　realistic　environment　is　possible，　a　paradox　may　exist．　For

264　　　　　　　　　　　　　『明大商学論叢』第82巻第1号　　　　　　　　　　　　（264）

and　functional　equations．　It　should　be　clearly　noted　that　the　original　Sato　model

deals　with　an　asymmetric　differential　game　model　which　generally　has　no　clear　cut

analytical　solutions．　Most　books　on　differential　garnes　do　not　deal　with　asymmetric

games　at　all；hence，　the　more　complete　solutions，　particularly　under　the　closed　Ioop

strategy，　may　exist　which　may　be　very　different　from　what　the　original　Sato　model

presented．　To　verify　the　validity　of　the　original　Sato　model，　we　may　have　to

employ　simulation　analysis．　It　seems　that　the　solutions　developed　in　the　original

Sato　model　for　the　closed　loop　strategy　may　not　really　be　the　standard　feedback

solutions　as　claimed．　This　presents　a　further　challenge　for　research．　In　addition，

we　may　extend　this　model　to　analyze　three　countries　at　a　different　stage　of

development　in　technological　efficiency；or　an　application　of　this　model　to　other

industries　such　as　home　electronics　may　also　be　interesting　for　future　studies．

MATHEMATICAL　APPENDIXCountry　A’s　problem：

鮒捌P（Y）距卸一（・一・）α聴肋　　　　　　　　　　　　　　　　　　　　　　　　Y・・　UA　s．　t，　UA・＝・iPA（TA）

Country　B’s　problem：

　　　　　　　　　　　　　　　M諮び・t［P（Y）距我一・s（・T・，・u・）］・dt

　　　　　　　　　　　　　　　　　　Y．　　　s．　t．TB＝・a／v（γTA），

where　P（Y）＝the　world（inverse）demand　function

Y＝YA十YB＝Country　A’s　Y十Country　B’s　Y

TA＝technical　progress　factor　of　Country　A

TB＝technical　progress　factor　of　Country　B

S　＝cost　of　developing　TA

θ＝cost　sharing　parameter　of　Country　B

　　　　Oくθ＜1

γ＝the　diffusion　parameter　of　TA　for　Country　B　by　Country　A．

Consider　an　extreme　case’thatθ　＝0，　i．e．，free　rider＝Country　B；then　Country　B’s

profit　function　will　always　be　larger　than　that　of　Country　A’s　provided　that

（265）．　　　　　　　Intra－industry　Trade　and　International　Technology　Competition　　　　　　　　　265

TB＝ψ（γTA），special　case　of　this　being　TB＝γTA，γ＝1

Another　special　case　is　θ＝1；i．e．，Country　B　pays　everything　to　Country　A．　In

this　case，　Country　A’s　profit　tends　to　always　be　larger　than　that　of　Country　B．

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　When　O〈θ＜1，　then　we　have　various　possibilities　ranging　from　YA芝　Y，　depending

upon　the　types　of　strategies．　Cases　described　in　the　model　are　by　no　means　all

possible　solutions　but　are　the　siMplest　cases．　We　have　assumed　in　actual

deterr【iination　that　the　demand　function　is　linear　and　the　cost　function　is　quadratic

which　gives　a　quadratic　dynamic　game　model．

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