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Chng trnh Ging dy Kinh t Fulbright Kinh t vi mo Nhap mon Ly thuyet tro chiNien khoa 2004 2005 Phan 1

GII THIEU LY THUYET TRO CHI

VA MOT SO NG DUNG TRONG KINH TE HOC VI MO

Cho en nay, chung ta a nghien cu bon hnh thai cau truc th trng c ban la canhtranh hoan hao, oc quyen, canh tranh oc quyen, va oc quyen nhom. Nguyen tac toia hoa li nhuan cua cac doanh nghip hoat ong tren 3 loai th trng au la quy tacquen thuoc MR = MC. Trong khi o, th trng oc quyen nhom (oligopoly), moidoanh nghiep tren th trng co mot the lc nhat nh, ong thi ton tai tng tacchien lc (ve nh gia va san lng chang han) vi nhng doanh nghip khac thcong thc MR = MC khong con thch hp na. V vay, e nghien cu ng x cua cacdoanh nghip trong loai hnh cau truc th trng nay, chung ta phai s dng mot cong

cu co kha nang phan tch c nhng tng tac chien lc cua cac doanh nghip thamgia th trng. Cong cu o la ly thuyet tro chi.1Ly thuyet tro chi nghien cu cac tnhhuong ra quyet nh co lien quan ti nhieu ngi va cac quyet nh cua moi ngi anhhng ti li ch va quyet nh cua nhng ngi khac.

Co mot so phng phap phan loai tro chi. Neu can c vao kha nang hp ong va chetai hp ong cua nhng ngi chi th co the chia tro chi thanh hai loai: tro chi hptac (cooperative games) va tro chi bat hp tac (non-cooperative games). Trong trochi hp tac, nhng ngi chi co kha nang cung nhau lap chng trnh (ke hoach)hanh ong t trc, ong thi co kha nang che tai nhng thoa thuan chung nay. Con

trong tro chi bat hp tac, nhng ngi chi khong the tien ti mot hp ong (khec) trc khi hanh ong, hoac neu co the co hp ong th nhng hp ong nay khoc che tai.

Phng phap phan loai tro chi th hai la can c vao thong tin va vao thi gian hanhong cua nhng ngi chi. Can c vao thong tin th cac tro chi co the chia thanh trochi vi thong tin ay u (complete information) hoac khong ay u (incompleteinformation). Tro chi vi thong tin ay u la tro chi ma moi ngi chi co the tnhtoan c ket qua (payoff) cua tat ca nhng ngi con lai. Can c vao thi gian hanhong lai co the chia tro chi thanh hai loai, tnh va ong. Trong tro chi tnh (static

game), nhng ngi chi hanh ong ong thi, va ket qua cuoi cung cua moi ngiphu thuoc vao phoi hp hanh ong cua tat ca moi ngi. Tro chi ong (dynamicgame) dien ra trong nhieu giai oan, va mot so ngi chi se hanh ong moi motgiai oan.2 Phoi hp hai tieu thc phan loai nay ta se co bon he tro chi tng ng vi

1 Ly thuyet tro chi t lau a tr thanh mot lnh vc quan trong cua kinh te hoc noi chung. No co ngdung rong rai trong kinh te hoc vi mo, v mo, tai chnh, quan tr, ngan hang, thng mai quoc te, chnhtr, khoa hoc ve chien tranh, ngoai giao noi chung la trong cac moi trng co tng tac chien lc.2 Neu moi ngi chi thi iem phai ra quyet nh ma biet toan toan lch s cua tro chi cho en thiiem o th ta noi rang tro chi nay co thong tin hoan hao (perfect information), bang khong chung ta

noi rang tro chi co thong tin khong hoan hao (imperfect information).

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bon khai niem ve iem can bang, trong o khai niem can bang sau manh hn khainiem can bang trc theo chieu mui ten (xem Bang 1).

Tnh ong

Thong tin ay u Can bang Nash NE Subgame Perfect Nash Equilibrium -SPNS

Thong tin khong ay u Bayesian Nash Equilibrium - BNE Perfect Bayesian Equilibrium - PBE

Bang 1: Bon he tro chi va cac khai niem can bang tng ng

Phan 1: Tro chi ong vi thong tin ay uDang thc cua tro chi nay la nhng ngi chi ong thi ra quyet nh (hay hanhong) e toi u hoa ket qua (co the la o thoa dung, li nhuan, v.v.); ong thi moingi chi eu bietrang nhng ngi khac cung ang co gang e toi a hoa ket quamnh se thu c. Ket qua cuoi cung cho moi ngi phu thuoc vao phoi hp hanhong cua ho.

Bieu dien tro chi di dang chuan tac (normal-form representation)

V du 1: The lng nan cua ngi tu

Gia s Giap va At b tnh nghi cung nhau an cap. Hai ngi b cong an bat ve onnhng cha the ket toi neu ca Giap va At cung khong nhan toi. Cong an mi ngh ramot cach nh sau khien Giap va At phai cung khai ung s that. Cong an se giamGiap va At vao hai phong tach biet, khong cho phep ho c thong tin cho nhau vathong bao vi moi ngi rang: Neu ca hai cung khong chu khai mnh pham toi thmoi ngi se b gi them 1 thang e tham tra va tm them chng c. Neu ca hai cungkhai nhan toi th moi ngi se phai ngoi tu 4 thang. Neu ch co mot ngi nhan toi conngi kia ngoan co khong chu nhan toi th ngi thanh khan cung khai se c hngs khoan hong va khong phai ngoi tu, trong khi ngi kia se chu hnh phat nang hn

la 5 thang tu giam. Cac kha nang va ket cuc nay c trnh bay mot cach chuan tactrong Bang 2 di ay.3

3 Mot cach khac, dang chuan tac cua tro chi tnh vi thong tin ay u co the c bieu dien di dangG = {S1, S2, , Sn; u1, u2, , un} trong o chung ta co the oc c cac thong tin ve so ngi chi (n),khong gian chien lc (hay cac chien lc co the - Si), va cac ket cuc (payoff) tng ng (ui).

V Thanh T Anh 2


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Giap

Khai Khong khai

Khai -4, -4 0, -5At

Khong khai -5, 0 -1, -1

Bang 2: The lng nan cua ngi tu

Chien lc ap ao (dominant strategy) va chien lc b ap ao (dominated strategy)

Trong cuoc chi nay, Giap va At moi ngi ch co the la chon mot trong hai chienlc (hanh ong): Khai hoac khong khai. Giap co the t duy the nay. Neu thang At

nhan toi ma mnh lai khong nhan toi th no trang an con mnh phai ngoi boc lchnhng 5 thang. Nh the th tha mnh cung nhan toi e ch phai ngoi tu 4 thang conhn. Roi Giap lai ngh, nhng ngo nh thang At no ngoan cng khong khai thmnh nen the nao nh? Neu no khong khai ma mnh cung khong khai th mnh phaingoi tu 1 thang, nhng ma neu mnh khai th mnh con c tha bong c ma. Nh vaytot nhat la mac ke thang At, mnh c khai bao la hn. Nh vay, du At co la chon thenao th phng an tot nhat oi vi Giap la khai nhan toi. Tng t nh vay, du At cola chon the nao th phng an tot nhat oi vi Giap la khai nhan toi. Noi cach khac,oi vi ca Giap va At th chien lc khai nhan toi la chien lc ap ao so vi chienlc khong khai; ngc lai, chien lc khong khai la chien lc b ap ao so vichien lc khai nhan toi.

Trong v du nay moi ngi chi ch co hai chien lc la chon, va v vay chien lc apao cung ong thi la chien lc tot nhat. Trong nhng bai toan co nhieu ngi chivi khong gian chien lc ln hn th e tm ra iem can bang cua tro chi, chung taphai lan lt loai tr tat ca cac chien lc b ap ao. Tuy nhien oi vi cac tro chiphc tap ieu nay khong n gian, va tham ch ngay ca khi loai het cac chien lc bap ao roi chung ta van cha the tm c iem can bang. Trong v du trnh bay Bang 3, co hai ngi chi, moi ngi co 3 la chon. Sau khi loai het cac chien lc bap ao chung ta van cha the tm c iem can bang. Xuat phat t han che nay cuaphng phap loai tr cac chien lc b ap ao, Nash a a ra mot khai niem canbang manh hn.

Trai Gia Phai

Trai 0, 4 4, 0 5, 3

Gia 4, 0 0, 4 5, 3

Phai 3, 5 3, 5 6, 6

Bang 3: Loai tr cac chien lc b ap ao va can bang Nash

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Trong v du Bang 3, can bang Nash duy nhat la (phai, phai) vi ket cuc la (6,6)nhng neu ch dung phng phap loai tr cac chien lc b ap ao th khong the ketluan c au la iem can bang.

Can bang Nash: Trong tro chi dang chuan tac G = {S1, S2, , Sn; u1, u2, , un}, to hpchien lc (s*1, s*2, , s*n) la mot can bang Nash neu, vi moi mot ngi chi i nao o,s*i (tc la chien lc do ngi th i la chon) la phan ng tot nhat cua ngi chi nayoi vi cac chien lc cua (n-1) ngi chi con lai (s*1, s*2, , s*i-1, s*i+1, , s*n) (kyhieu la s*-i). Noi cach khac, ui(s*i, s*-i) ui(si, s*-i).

Ve mat toan hoc, s*i la nghiem cua bai toan toi u:*

max ( , )i i i

i i

u s ss S

Trong v du cua Giap va At, iem can bang cua tro chi la (khai, khai) trong o

Giap va At cung khai nhan toi, va ay cung la can bang Nash duy nhat cua tro chinay.

Lu y rang v can bang Nash c tao bi nhng chien lc phan ng toi cua tat cangi chi (ng vi cac chien lc toi u cua nhng ngi chi con lai) nen no co tnhon nh va ben vng ve mat chien lc (strategically stable), ong thi no co tnh chatt che tai (self-enforcement) tc la moi ngi chi, khi cc ai hoa li ch cua mnh,se t nguyen tuan thu can bang Nash, ong thi ho khong he co ong c e di chuyenkhoi iem can bang nay.

Sau khi d bao c ng x cua nhng ngi chi khac th moi ngi chi chon chien

lc (quyet nh) e toi u hoa li ch cua mnh. Chien lc (quyet nh) nay v vayc goi la phan ng tot nhat (best response). Quay lai bai toan cua 2 ngi tu, nh alap luan phan tren, nhan toi la phan ng tot nhat cua ca Giap va At, va phan ngtot nhat nay khong phu thuoc vao hanh ong cu the cua ngi kia (nh lai rang nhantoi la chien lc ap ao)

Mot so ng dung cua tro chi tnh vi thong tin ay u

ng dung 1: oc quyen song phng Cournot (1838)

Gia s co 2 cong ty hoat ong trong th

tr

ng oc quyen song phng theo kieuCournot va cung san xuat mot sn phm ong nhat. San lng cua hai hang lan lt laq1 va q2. Tong cung cua th trng v vay la Q = q1 + q2. e n gian, gia s ham cauco dang tuyen tnh: P(Q) = a Q = a (q1 + q2). Cuoi cung, gia s rang chi ph canbien va chi ph trung bnh cua ca 2 hang bang nhau va bang hang so c, tc la: C i(qi) =c.qi , trong o c < a.

Bai toan cua moi hang la chon san lng e toi a hoa li nhuan

Bai toan dang chuan tac:

i) So ngi chi: 2

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ii) Khong gian chien lc: Si = [0, a]

iii) Ket qua

1(q1, q2) = q1[P(Q) c ] = q1 [ a (q1 + q2) -c]

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

nh ngha can bang Nash:

Cap (s1*, s2*) la can bang Nash u1(s1*, s2*) u1(s1, s2*) va

u2(s1*, s2*) u2(s1*, s2)

= (q11

*

211 ),(max

Ss

ssu

1, q2) = q1[a (q1 + q2*) -c] => q1 =

2

*

2qca 3

*

2

*

1

caqq

==

22

2

*

12 ),(max

Ss

ssu

= (q1, q2) = q2[a(q1* + q2) -c] => q2 =

2

*

1qca

va9

)( 2*2

*

1

ca ==

(a-c)

(a-c)/2

(a-c)/3

q2

q1(a-c)/3 (a-c)(a-c)/2

Hnh 1: Can bang Nash cua canh tranh oc quyen song phng Cournot

Bay gi xem xet trng hp 2 cong ty cau ket vi nhau va hoat ong nh 1 cong tyoc quyen. Khi ay, chung phai giai chon Q sao cho:

[0, ][ ( ) ] [ ]

mQ a Max Q P Q c Q a Q c

= =

1 2

** * * *

12 2 4 3m

m m m

Qa c a c a cQ q q q

= = = = < = =

*

2q , trong o gia s rang hai

hang chia oi san lng.

V Thanh T Anh 5


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Thay2 2

* * * * *

1 2 1 2 1

( ) ( )

4 8 9m m

a c a c a cq q

= = = = > = =

*

2 ; trong o

*1 va *2 la li nhuan cua hai cong ty khi chung canh tranh vi nhau theo kieu

Cournot.

4

*

2

*

1

caqq mm

==

9

)( 2*2

*

1

ca ==

T nhng ket qua nay co the thay rang hai cong ty co ong c cau ket vi nhau ekiem che san lng va va chia se li nhuan oc quyen. Mot cau hoi at ra ay lalieu thoa thuan nay co on nh va co kha nang t che tai hay khong?

Tai iem can bang cua th trng oc quyen (Em), o co dan cua cau vi gia|Ed| > 1%Q/%P > 1, hay %Q > %P. V vay neu mot doanh nghiep tang san lng 1lng u nho th mc giam gia se nho hn mc tang san lng; ieu nay co ngha ladoanh nghiep tang san lng se co li va tat nhien doanh nghiep gi cam ket se bthiet.

a

a/2

Qa/2 a(a-c)/2

MR

Em

Hnh 2: S khong ben vng cua thoa thuan cau ketMot cach khac, chnh xac hn, e thay rang thoa thuan cau ket khong co kha nang tche tai la s dung phep chng minh bang toan.

Ta biet: 1 = q1[a c (q1 + q2)].

Bay gi gia s4

*

22

caqq m

== => ]

4

)(3.[ 111 q

caq

=

111

1

1 24

)(3

4

)(3q

caqq

ca

dq

d

=

=

V Thanh T Anh 6


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Neu 04 1

1*

11 >

==

q

caqq m

Nh vay, doanh nghiep 1 co the tang 1 bang cach tang q1. Trong khi ay:

*m2 = qm2[a c (q1 + qm2)] = 04

)(3

4 1

*

2

1

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