ly thuyet tai chinh 2

8/14/2019 ly thuyet tai chinh 2

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Chng trnh Ging dy Kinh t Fulbright Kinh t vi mo Nhap mon Lythuyet trochiNien khoa 2005 2006 Phan 2

V Thanh T Anh 1

GII THIEU L YTHUYET TROCHI

VAMOT SONG DUNG TRONG K INH TEHOC VI MO

Phan 2: Trochi ong vi thong t in ay uTrochi ong (dynamic game) dien ra trong nhieu giai oan, vamot songi chi sephai hanh ong moi mot giai oan. Trochi ong khac vi trochi tnh mot sokhacanh quan trong. Thnhat, trong trochi ong, thong tin mamoi ngi chi cocvenhng ngi chi khac rat quan trong. Nh Phan 1 aphan biet, mot ngi cothong tin ay u(complete information) khi ngi ay biet ham thoa dung (ket cuc -payof f) cua nhng ngi chi khac. Con mot ngi cothong tin hoan hao (perfectinformation) neu nh tai moi bc phai ra quyet nh (hanh ong), ngi ay biet ctoan bolch scua cac bc i trc ocua trochi . Thhai, khac vi cac trochi

tnh, trong trochi ong mc oang tin cay (credibi lity) cua nhng li ha (promises)hay e doa (threats) layeu tothen chot. Vacuoi cung, etm iem can bang cho cactroong, chung ta phai van dung phng phap quy nap ngc (backward induction).

Tr ochi ong vi thong tin ay uvahoan hao

V du1: Mot tr ochi tng tng

Thtng tng mot trochi ong vi thong tin ay uvahoan hao vacocau truc nh

hnh ve. Tai moi nut hoac A hoac B phai ra quyet nh. Khong gian hanh ong cua hochgom hai khanang: hoac chon trai (T), hoac chon phai (P). Nhng con songon cuacac nhanh trong cay quyet nh chket quathu c cua hai ngi chi, trong osotren laket quacua A.

etm iem can bang cua trochi nay, chung ta khong thebat au tgiai oan autien, mangc lai, chung ta sedung phng phap quy nap ngc, tc labat au tgiai

oan cuoi cung cua trochi.Lu ylaphng an toi u cho ngi chi thnhat laket cuc T , oA c 3 vaBkhong c g. Con phng an toi u cho B laket cuc P , trong oB c 2 vaAkhong c g. Nhng cahai ket quanay eu sekhong xay ra. Tai sao vay?

Neu trochi keo dai en giai oan 3 th A chac chan sechon T (v 3 > 2). Con neu Bc ra quyet nh giai oan 2 vabiet ieu nay chac chan sekhong chon P machon

B

A

A

PT

PT

T P

2

0 11 3

022


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V Thanh T Anh 2

T (v 1 > 0). Vagiai oan 1, A doan trc c nhng hanh ong ketiep cua cahai ngi nen chac chan sechon T (v 2 > 1).1

Bay gichung ta quay lai thao luan van emc otin cay cua li ha hen hay e doa.Giastrc khi bat au chi , A enghvi B nh sau. Trong lan chi au tien anh nen

chon P. Neu the, khi en lt toi th toi sechon P , varoi trong giai oan cuoi cung anhsechon P emoi chung ta cung c 2. Lieu A conen tin vao li engh(ha hen)bang mieng nay cua B hay khong?2 Neu ay latrochi xay ra mot lan vamuc ch cuamoi ngi chi n thuan chlatoi a hoa li ch cua mnh th cau trali hien nhien lakhong. Lydo laen giai oan 2, B biet chac laneu A oi yvachon T th anh ta sekhong c g, con A sec 3 (laket cuc tot nhat cua A). Lng trc ieu nay, B chi A chon P lasechon T ec 1. ng trc tnh huong nay, vi nhng thong tincho trc vaneu A langi duy lyth chac chan A sekhong dai g nghe theo li hahen ngon ngot cua B. Ket qualaA sechon T trong giai oan au tien nh chung ta aphan tch tren. Noi mot cach ngan gon, nhng ha hen vae doa trong tng lai ma

khong ang tin cay sekhong hecotac ong g, dulanhonhat, ti ng xcua nhngngi chi trong giai oan hien tai. Trong mot phan khac, chung ta senghien cu tnhhuong trong oli ha/ e doa ang tin cay vado ocoanh hng en hanh vi cuanhng ngi chi ngay trong giai oan hien tai.

V du2: Mohnh oc quyen song phng Stackelberg (1934)

Nhlai trnh tthi gian cua trochi nay nh sau:

1) Hang 1 chon san lng q1 02) Hang 2 quan sat q1 roi sau ochon san lng q2 03) Hai hang san xuat vi san lng q1, q2 vali nhuan tng ng la1 va21(q1, q2) = q1[P(Q) c] ; Q = q1 + q2

2(q1, q2) = q2[P(Q) c] ; P(Q) = a Q = a (q1 + q2)

trong ohang soc lachi ph can bien, ong thi lachi ph trung binh cua ca2 hang.

etm iem can bang cua trochi nay, chung ta lai ap dung phng phap quy napngc bang cach bat au vi hang th2. au tien chung ta phai tm ham phan ng totnhat cua hang 2 oi vi quyet nh san lng q1* cua hang thnhat trong giai oan 1 :

Max 2(q1, q2) = q2[a c q1* - q2] => q2 = (a - c q1*)/2

q2 0

1 eyrang phng phap quy nap ngc c sdung ay mot cach dedang lanhcau truc thong tinay uvahoan hao cua bai toan (tng tng) nay. Trong cac bai toan thc te, cau truc thong tin thngphc tap hn nhieu.2 V lahp ong mieng nen nokhong thebchetai nhtrong tai.


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V Thanh T Anh 3

Lu yrang vemat hnh thc th ham phan ng q2(q1* ) ay giong nh trong mohnhCournot. Tuy nhien, comot iem khac biet quan trong latrong mohnh Cournot, q1* lamot giatrgianh, con trong mohnh nay, khi ra quyet nh q2 hang 2 aquan satc vabiet giatrcua q1* .

V ay labai toan vi thong tin ay uvahoan hao nen hang thnhat cotheat mnhvao vtr cua hang thhai vado vay biet rang neu mnh quyet nh san lng laq1* thhang thhai sesan xuat q2 = (a - c - q1* )/2. V vay, trong giai oan 1, hang thnhat sechon q1 sao cho

Max 1(q1, q2(q1)) = q1[a - c q1 q2(q1)] =2

1

1

qcaq

Li nhuan tng ng la:

9

)(

16

)(

9

)(

8

)(

2*

2

2*

2

2

*1

2

*1

caca

caca

cS

cS

=>

=

=>

=

Cau hoi at ra latai sao hang 1 cotheat c mc san lng vali nhun tngng vi mc san lng vali nhun oc quyen trong khi hang 2 tham ch con khongat c mc li nhuan trong oc quyen song phng Cournot? Cau trali khongthuan tuy chnam trnh tthi gian maquan trong hn lado thong tin. Trong v dunay, cahai hang eu biet nhieu thong tin hn so vi trng hp oc quyen songphng Cournot: Hang 2 cothequan sat quyet nh vesan lng cua hang 1, con hang

1 biet lahang 2 biet san lng cua mnh. Tuy nhien hang 1 cothesdung thong tin bosung nay elam li cho mnh trong khi hang 2 khi cothem thong tin lai bthiet hai.Hay noi mot cach chnh xac hn, viec hang 2 lam cho hang 1 biet lahang 2 biet sanlng cua hang 1 lam cho hang 2 bthiet. ethay ieu nay, giasbang mot cach naoo, hang 2 gay nhieu thong tin lam cho hang 1 khong biet c lalieu hang 2 cobietsan lng cua mnh hay khong. Khi ay, bai toan trthanh tng tnh vi trng hpoc quyen Cournot trong o2 ben quyet nh san lng makhong hebiet san lngthc tecua ben kia (thong tin khong hoan hao)

V du3: Mac caluan phien(Rubinstein sequential bargaining) xem bai oc them.

Trochi ong vi thong tin ay unhng khong hoan hao(xem bai oc them)

Trochi lap lai (repeated games)

Muc ch cua tieu muc nay laxem xet lieu cac e doa hay ha hen tng lai ang tincay anh hng thenao ti hanh vi hien tai cua nhng ngi chi.

4

2

*

2

*

1

caq

caq

=

=


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V Thanh T Anh 4

V du1: Thelng nan tr ong tr ochi lap hai gi ai oan

Quay lai bai toan lng nan cua ngi tuc trnh bay di dang chuan tac nh trongbang ben.

Can bang Nash duy nhat la(khonghp tac, khong hp tac) vaket cucla(1, 1). Bay gigiastrochinay (goi latrochi giai oan stage game) c lap lai lan thhai, bang ket quac trnh baytrong bang di ay.

Can bang Nash duy nhat van la(khong hp tac, khong hp tac) vaket cuc hp tac van khong at c

nh lamot iem can bangNhan xet:

- Neu trochi giai oan (stage game) chcomot can bang Nash duy nhat th neu trochi ay c lap lai nhieu lan th cung sechcomot can bang Nash duy nhat, olaslap lai can bang Nash cua trochi giai oan.

- Rorang laneu trochi nay c lap lai nhieu lan th thiet hai tviec khong hptac serat ln. Cau hoi at ra lalieu cocach nao ethiet lap shp tac hay khong?ay chung ta tam thi khong quan tam ti kha canh ao c valng tam cuamoi ngi chi machxem xet thuan tuy veong c kinh tecua ho.

V du2: Thelng nan trong t rochi lap vnh vi enBay gigiastrochi c lap lai mot cach vnh vien. Chung ta sexem xet khanangmot e doa hay ha hen tng lai ang tin cay anh hng thenao ti hanh vi hien taicua nhng ngi chi?

Nhlai cong thc tnh hien giacua thu nhap, trong omot ngi nhan c 1 tronggiai oan 1, 2 trong giai oan 2 v.v. Tong thu nhap cua ngi otnh theo giahien tailaPV = 1 + 2 + 23 + ; trong o lanhan tochiet khau (discount factor).

Bay gichung ta sechng minh rang ngay cakhi trochi giai oan chcomot canbang Nash duy nhat th van cocach ebuoc nhng ngi chi duy lyhp tac vi nhau,

vi ieu kien

uln. Cach thc eat c shp tac nay lathc hien chien lc trng phat (trigger strategy) mathc chat lamot li e doa traua ang tin cay oivi nhng hanh vi vi pham hp ong. Chien lc trng phat nay c thc hien nhsau:

Ngi 1Khong hp tac Hp tac

Khong hp tac 1 , 1 5 , 0Ngi2

Hp tac 0 , 5 4 , 4

Ngi 1

Khong hp tac Hp tac

Khong hp tac 2 , 2 6 , 1Ngi2

Hp tac 1 , 6 5 , 5


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V Thanh T Anh 5

- Trong giai oan 1, chon hp tac- Trong giai oan t, tiep tuc chon hp tac chng nao trong (t-1) giai oan trc

ngi kia cung chon hp tac- Chuyen sang chi khong hp tac neu trong giai oan (t-1), ngi kia phabo

hp ong chi hp tac

Gias trong suot (t-1) giai oan au tien, cahai ngi chi eu tuan thuthoa c vachon hp tac . Nhng tai giai oan tht, mot ngi toan tnh viec vi pham thoa c vthay cai li trc mat. Khi ay, ngi nay phai so sanh 2 giatrthu nhap kyvong cuahp tac vakhong hp tac.

Neu trong giai oan t ngi ay khong hp tac th ngi ay c 5, vat(t+1) tringi kia sechon khong hp tac etrng phat ngi nay, vakhi ay phan ng tot nhattng ng cua ngi nay cung selakhong hp tac. Nh vay, tong giatrkyvong thunhap cua ngi ay theo hien giala:

(1)

Khanang th2 langi ay tiep tuc chon hp tac. Khi ay, tong thu nhap cua anh ta theohien giasela:

(2)

So sanh (1) va(2) ta thay

+

15

1

4CC

PVPV

4 5(1-) + = 5 -4

1/4

Nh vay, neu 1/4 th chien lc trng phat lamot can bang Nash. Noi cach khac,vi uln (tc lanhng ngi chi chiet khau tng lai ut) th khi theo uoi muctieu vklatoi a hoa li ch cua mnh th tat cangi chi eu coong c ton trong

thoa c hp tac.V du3: Tr lai vi oc quyen song phng Cournot

Chung ta abiet rang trong trng hp oc quyen song phng Cournot:

qc1* = qc2*=(a-c)/3 vado vay QC* = 2(a-c)/3 > Qm* = (a-c)/2 ( = mc tong cau khi haidoanh nghiep cau ket lung oan th trng oc quyen). Nh vay, hai hang nay cothe

]1

5[

...1.1.5.

1

11

+=

+++=

+

t

C

ttt

C

PV

PV

+=

+++=

+

14

...4.4.4.

1

11

tC

ttt

C

PV

PV


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V Thanh T Anh 6

ap dung chien lc trng phat eat c shp tac trong san xuat. ekiem tra laimc ohieu cac noi dung trnh bay v du2, chung ta cothelam mot bai tap nhosau.Giastrochi Cournot nay c lap lai mai mai, hay tm giatrtoi thieu cua egiaiphap hp tac lamot can bang Nash (SPNE)?

Chien lc trng phat nh sau:

- Bat au chi bang viec chon mc san lng Qm/2* (=(a-c)/4) trong giai oan 1- Neu trong (t-1) giai oan au tien, ben kia chon Qm/2* th tiep tuc chon Qm/2* .

Bang khong th chuyen sang Qc/2* (= (a-c)/3) mai mai.

Giasgiai oan t, hang 1 toan tnh chuyen phavthoa c ban au. Hang nay bietlahang 2 sechuyen sang chon q2* = qc2* ketgiai oan th(t+1). V vay, hang 1ng trc hai la chon:

- Phavthoa c:

..)(

....21

11

+++=

+++=

+

CCd

t

C

t

C

t

d

tC

)1

(1 CdtC

+=

Neu hang 2 tiep tuc chon hp tac trong giai oan t, tc latiep tuc chon q2* = Qm/2* = (a- c)/4 th qd1* semax qd1[a - c - qd1 (a-c)/4] => qd1* = 3(a-c)/8 => d = 9(a- c)2/64

- Ton trong thoa c:....

11+++=

+

m

t

m

t

m

tC

=

1

1 mtC

So sanh CC :

Mot lan na chung ta lai thay laneu uln (tc lanhng ngi chi chiet khau tnglai ut) th khi theo uoi muc tieu vklatoi a hoa li nhuan cua mnh th hai congty cung coong c ton trong thoa c hp tac.

17

9

178164)1(8172

964

)1(9

8

1

9

)(

164

)(9

)1(8

)(

11222

=+

+

+

+

cacaca

Cdm


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V Thanh T Anh 7

Tai l ieu tham khao

Robert Gibbons, Game Theory f or Applied Economists, Princeton University Press, 1992

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