dynamics and stability of constitutions, coalition
TRANSCRIPT
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Aeria Ei Review 2012, 102(4): 14461476hp://x.i.r/10.1257/aer.102.4.1446
1446
C h b h . N, h
w w f h . Y,
h b h w-k , h - h b . F ,
h b h j h
h b z -
. I , h h j b h
w h . M b , b
h, , z , z
h b h h.
W b wk h -
. C b .
I sae. A wk bh . I , ( ,b h ) hw h (.., whh b h h
Dynamics and Stability of Constitutions,
Coalitions, and Clubs
By Daron Acemoglu, Georgy Egorov, and Konstantin Sonin*
I yai lleive eisi aki, urre eisis eeriehe uure isribui pliial pwer a iuee uure ei-sis. We evelp a eeral raewrk suy his lass prb-les. Uer ayliiy, we haraerize yaially sable saes as
uis he iiial sae a bai w eeral isihs. Firs,a sial arraee is ae sable by he isabiliy alera-ive arraees ha are preerre by sufiely pwerul rups.Se, efiey-ehai haes ay be resise beause
urher haes hey will eeer. We use his raewrk aa-lyze yais pliial rihs i a siey wih iere ypes exreis views. (JEL D71, D72, K10)
* A: D E, Mh I Th, 50 M D, B E52,R 380B, Cb, MA 02142-1347 (-: @.); E: D M E D S, K Sh M, Nhw U, 2001 Sh R., Jb C,R 539, E, IL 60208 (-: [email protected].); S: Nw E Sh, 47Nkhk ., O 922, Mw, 117418, R (-: k@.). W hk h , Jh D, Mhw Jk, Rb Pw, h ASSA 2008(Nw O), h 2008 G Th W C, Bk, Cb, C I Th,H, P, Nhw, S, Y . A kw - h NSF, AFOSR, h C I A Rh.
T w , h h://../10.1257/.102.4.1446.
http://dx.doi.com/10.1257/aer.102.4.1446http://dx.doi.com/10.1257/aer.102.4.1446 -
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1447AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
; E 1 2). O qb wh w-k. U
h C- , w h hz h
(yaially) sable saes. A qb b
whh h b (s0) h s0. W hw h h b h .
Ahh h h -
b, bh wh h-
z b . Th hz h b h
w-k wh h w
() h h h, (sabiliy axi). W w h h - h h h w . W hz h
, , h wh h h whh h q b (Th 1). W hwh wh , h b b w1,2, .
O Th 2. U h h () h 1, () h () h , h qb -
. C, ,h h h h qb -
b .Bh hh b hhz h b , hh h b
.1 Th hh
b whh w ,
w, b h b h wh h w (whh -q k , bw). W b h j h z
.2 W h , hw, h h h
b h hh
( h, qb, q wh hw h b wh h ; bw).
A h h h k ie
-k bh h -k w
1Th h h wh h h w h h h h.S w w ( , bw ), h b wh w-k wh ( E 3, 4, 5 h A).
2O h b h h
h , , h, b A Rb (2000, 2006) Lzz P (2004). Th wk h wh b, , h h, b (hw, w h b ). Th b h h h h (.., , h bk bk wh ).
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1448 tHE AmERIcAn EconomIc REVIEW JUnE 2012
h h h w
h h k. Th k w -
. F, (, , b) b b h b w h h
, b b h b sable h b w . T wh
b, w h h b h h w
h w h. S, b b
.., h b P b h h (Th 3).
O , Th 4, h
( Th 1 2) h wh b (.., b ). I , hw h h wh () - -k ( h w ). Th h j ,
b h h A. Th
4 hw h bh b w
; , Th 1 2
whh b .
Bw, w w h h h-
. W wh h h bw
w h hh -
. W h b , whh w S V.
Example 1: C h w ,E, h ,
m, h . Th h wh b
w: (1) b h a, whhE, wh hm; (2) h , whhmh w ; (3) , whmb f E. S
wE() < wE(a) < wE() , wm(a) < wm() < wm() .
Th hEh hh h h
b h (.., b bm ).O h h h, m h
w- b h. Bh h
(0, 1). S a,, , b . I b h,E whh w w;
bh ,m .
U , b , () = . I , b , , h w b
h, () = . Th, , a,Eh , hw h w , h E
UE(rer) = wE() + wE()_1
.
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1449AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
IE a , UE( rer) = wE(a)/(1 ).I , h UE( rer) < UE(rer), k. Wh w-k, hw ( ), hUE( rer) > UE(rer). I h , (a) = a. Th bh
. F, a b b h b h ,, whh b h wh w a. S, bhEmw
b b h a, h b a P -
. I h h b wh w-
k (wh , b; wh , bh a b).
Example 2: C h h hw h b w -
w. A wh
M wh , , h
. A , h S Ab I
k h. A h h , Tk,
S, A, E wh M h
. Bh
b b , , b . S
Ab I h h w wk
h , wh Tk b I h b -
b h - h h
w h h .3 S
h Tk w w
h h .T h h b w,
n k . A s h
Zwh h h h
h . I h . S h h h wh h h , h (.., bh wh h
k k b). W ,.., j j , h wh h bh h
wh w h h h h .Th hh , w, . I
h h h
h h- b b -
h h. M, bh h hh
b h .4 I S V, w
h h .
3O , Sh (1985), h f bw ,
Rb Lb (2008) R (2007).4F , Tk h Ib qk h b h (hh h w ), whh wh q h h hh . Fh, h f k, wh , whh wh .
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1450 tHE AmERIcAn EconomIc REVIEW JUnE 2012
Th b h q: w h h -
h h wh h b
h? Th b z
wh wk b h q
h ( Bb Jk 2004). Sh P . O , hw, hhh h wh h
h b b; .., wh j
h w h h .
Rb (1999) Bb, Mh, Sh (2001) b w j . Rb (1999) b whn, wh b j ,
- , b h
{1,2, ,k} k w. Bb, Mh, Sh(2001) b whh b h b w .5 L(2009), wh h
, h . Th h A
Rb (2000, 2006) Lzz P (2004), h - b Bb Jk(2004), b wk.
Tw h Chw (1994) G Jh (2005).Chw wh b
h b z h h
bw w h, b. I Chw , hw, h h-
z b.6 G Jh wh
. Th hw h h
h b h , h h qb b -
wh h . I , P
b , b q qb
k wh 1. W
hz ( q) , whh G Jh ( , wh , w h h -
b). F, b h ,wh G Jh, h 1, h
(.., h b h ).F, wk h -
b h.7A bw h h
h, b , w h
h j ( j) h b h h w
5Bb, Sh, Zh (1991) b q, h b w -
b b ( h h q) . Th h h b , wh h, h , h w q q q .
6Th k bw Chw b h A.7O , , .., M (1997); R Vh (1997, 1999); S
W (1998); Kh R (2003). O b h, Ek . (1999) Sh (2002).
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1451AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
h wh h j. Th wh h -
- b b h . I ,
h wk h b b (R Vh 1997,1999), wh w h h w.8
Th h z w. S I h . S II . I S III, w
h (-) Mk qb h bh h q bw
h qb h hz S II. S IV
wh b , wh S V
h h E 2. S VI .
A A ; , ,
h A.
I. Environment
Th . T , b ( 1).Th saes whh w b . Thh h , |X| h b X, | | | | h b - , . S bh
, h b w h -
k (.., z , h -j, h wh w ). Ahh
b , b b w- (b b ) h h h k, b .
Th b s0. Th b h - h h b N . F 1, h s . A X alii, w h b . Eh s hz b ({wi(s)}i,s). H, h s , wi(s) () i . P s b b h wiialiis s, s, (b ) b . Th w
z , h wh j j- , w. F , s j q
k, s b h j; s - i , s h i.
9 S s h , h k .10
8Oh wk Bk W (2000), wh h b; Jh Sh (2001), wh hw h h q j j b h h ; A, A, E (2005),wh h b EU ; B B (2003), wh h h EU .
9
P z b h s , h wh k ,hw k , . Th b h - . W w hw h h h qb , j s .
10O w h wh , s s, h b h w .
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1452 tHE AmERIcAn EconomIc REVIEW JUnE 2012
Thh h , w h w .
ASSUMPTION 1 (W C):Fr ay sae s ,s saisfes
()I X, Y, X Y, a Xs he Ys.
()IX,Ys, he X Y.
P () h X w s, h h z h w h. P () h b hw j w h . Is= , s ex-eusly sable. N hz whh
h b .
W h w b . Fx,y , w w
(1) x y i : wi(x) = wi(y).
I h w x ypay-equivale, equivale. M
h b z. F z , z b
(2) y z x {i : wi(y) wi(x)} z.
I,y z x h h h w (
z) wh h b wk y x. N h - b z. F, b . I ,wi (y) wi(x) h i wh y h h
x. Whh h h w h
wh. S, h z - k h b h q. I
h h . Th, h z z whh h wk y x w
h w , whh . Wh h b
, q (2) h, w hy weakly preerrexz. I h
h , h h h y x, h h w b xy h
h w , h b
y h x. R z b
(3) y z x {i : wi(y) > wi(x)} z.
I(3) h, w hy srily preerrexz.11
11R q ; xy y z, hx z. I , h b zz b . Nh, x,z , w hxz x, wh z , w hxz x. F A 1 w h h x,y,z ,y z xxz y, y z xxz y.
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1453AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
Th j w
.
ASSUMPTION 2 (P): Pays {wi(s)}i, s saisy he llwi
prperies:
() Fr ay sequee saess1,s2, ,ski,
sj+1 sj sj r all 1 j k 1 s1 sk sk.
() Fr ay sequee saess,s1, ,ski S wihsjs sr1 j kasj sl 1 j < l k,
sj+1 s sj 1 j k 1 s1 s sk.
mrever, i rx,y,s Swe havexs say s x, hey s s.
A 2 j (b wk h ). P () h y xx, z y y,
xz zh , h h h , w h . P () h y s x, xs z, z s y( h x,y, z -q). A h, h y s x,z s y,xs z.
12 I q
h b .13
Ahh A 1 2 , h
b hz . M -
, h ( Th 4 h A). I A 1 2, w b q b h w()q.
ASSUMPTION 3 (Cb): Fr x,y,s suh ha xs s, y s s, ax y, eiher y s x r xs y.
A 3 h w xy s( s), h q, hxy s-b. Th - b q qb.
II. Axiomatic Characterization
B h - , w -
b hz b . Th h w
12Nh A 2 b h h. E 6 7 h A h h wh h 2() 2() .
13T w q h s,x,y z,y s x,xs z y s z. I, h whz = s.
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1454 tHE AmERIcAn EconomIc REVIEW JUnE 2012
. F, h h k h h
k h
- . S, h h -
h hz h qb h
h . I , , Th 2, w k h hz.
Th k h b hz hwih su-
fiely rwar-lki behavir, a iiviual shul wish rasi a
sae ha will uliaely lea aher sae ha ives her lwer uiliy. Th b
h b h hz (axiaially) sable saes.M , hz
h h , : b s h s0. W h w h .
AIOM 1 (Db): I x,yare suh ha y = (x), he eiher y =x ry xx.
AIOM 2 (Sb): I x,yare suh ha y = (x), he y = (y).
AIOM 3 (R): I x,y,zare suh ha z xx, z = (z), a z xy, hey (x).
A h h wh w h b. A 1
q h h h x h y h w h h . A 2 -
h b b; b,
b h b . A 3 h -
b q h h b z bhxy b w-
x, h h ky x.14 N h wh h , h h .
W h h h bw b .
DEFINITION 1 (A Sb S):Le { : : saisfesA 13}. A sae sis (axiomatically) stable i(s) = s r se .the se sable saes (fxe pis) r appi is = {s : (s) = s}a he se all sable saes is = {s : (s) = s r se }.
Th h bh h b h w
Th 2, whh bh h q bw qb h
14A 2() h y xx z xy, h z xx. Th, A 1 , h hqz xx b A 3.
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1455AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
( S III bw) b . A Th 1 A A.15
THEOREM 1 (A Chz Sb S):Suppse Assupis 1
a2 hl. the
() the se is epy. tha is, here exiss a appi saisyi Axis 13.
()Ay a be reursively srue as llws. orer he saes as{1, ,| |}suh ha r ay 1 j < l | |, ljj. Le(1) = 1.Fr eahk= 2, , | |, efe
(4) k = {s {1, ,k1} : s k ka(s) = s}.
Th
k k = (5) (k) = { . s k: z kwih z k s k (I here exis re ha es k suh haz k wihz ks, pik ay
hese; his rresps uliple uis).
(iii) the sable ses ay w appis1,2 iie; i.e., 1 = 2 = .
(iv)I, i aii, Assupi 3 hls, he r ay w appis1a2i, 1(s) 2(s) r all s .
Th 1 hz h h A 13. I, A 2() h h 1 h h h h s wh s 11. Tk 1
b, w h { 1, , | |} j 2 h h. Th, w h k ,k= 2, , | |, h b h k(h , s h h (s) = s s kk). Wh h k , h b h k( k) b b w . I h ,w h (k) = k. Wh k , h h b h(k) = s h s. I ( h --), h hz hhh h
b hz h I: k b b
15Th h b wk . P () A 2 b b bh w : Fr ay sequee saes s,s1, ,sk i Swih sjs sr1 j k, sj+1s sj r all1 j k 1 wul iply s1s sk.
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1456 tHE AmERIcAn EconomIc REVIEW JUnE 2012
h b w k h sable (.., b h h k= ). Th h .
P () Th 1 hw h h b h h . F w 1 2 , b
h 1(s0) 2(s0) s0, b h h h . Th , h h b , q b h w .16 F, 4 hw h
wh A 3 h, b b
-q. I h w, s1= 1(s0) s2= (s0), h s1 s2 h h w , b h h
h .
W h h Th 1 wh h h,
wh w-k, b h
b b ( h ; .., t t). Th h h b h .
III. Noncooperative Foundations of Dynamically Stable States
W w b h - h
S I hz h Mk qb (MPE) h . Th h q bw h MPE h h
Th 1.W h . A
h , i z
(6) Ui() = (1 )=
ui( ) ,
wh (0, 1) . W
ASSUMPTION 4 (P):the sae pays i (6) are ive by
wi(s) s = s1(7) ui() = { . wi s s1F h i x, w h
wi < wi(x) .
A 4 :
whh h , h b w h h w
16I h A, w h w h, N-M b Chw . U A 1 2, bh wh .
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1457AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
h wh h . G z wi(s) > 0, A4 ; .., wi= 0 i. S w h 1, h h .17 I , ( ) b s h, wi(s) h h-
. Sb, h h - MPE.18
W : () q - h ; () . V q b bw; h q whh w .19 W
h q ,{s}s, prl. L Ksb b h s . Th, s
s : {1, ,Ks}
h s . Th, h s q , h q - (h Ks hh h q s). Is(k), h -wh w k h . A, s(k), h whh
. Th, h - h bh -
h w b - .
W k h w {s}s:
ASSUMPTION 5 (P): Fr eah s , e (r bh) he llwi wiis hls:
() Fr ay saez \{s}, here exissk : 1 k Ks suh has(k) =z.
() Fr ay playeri here exissk : 1 k Ks suh has(k) = i.
Th h h qs b h
h h q s w b - - k b h . W h s h s; h h h w
.
17M , _
= i,x|wi(x) wi|, whh h z . Th
_
, h 0< 1 h h Th 2 h > 0. Th , whh h A, h h h b wh .
18E 4 5 h A h h q(7), (-) qb . Wh h b
, h b b. A (.., h h ) wh w wh h .
19Th q w MPE wh h h q qb. A, E, S (2009) qb, Mk b h qb, whh qb bh wh wh q .
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1458 tHE AmERIcAn EconomIc REVIEW JUnE 2012
I h b, = 0, s0 (h h - h ). Sbq ( 1), h w:
Periodb wh s1 h h . Fork= 1, ,Ks1, h kh Pk, w. Is1(k),
h Pk,= s1(k). Is1(k), h s1(k) h Pk, . IfPk, s1, h h q bwPk, s1(w w hw
h h q h h qb ). Eh yes( Pk,) ( s1). L Yk, h whyes. IYk, s1, h Pk, ; hw (Yk,s1), j. IPk,= s1, h w h - h h Pk, j.
IfPk, , h s= Pk,k , h . IPk, j h bPk,= s1 k< Ks1,h h 2 wh k b 1; k= Ks1, h s= s1, h .
Attheendoftheperiod,eachplayerreceivesstagepayoffui().
A MPE h h b qb
(SPE) wh - . H - h s b b, h - , w , -
h ( h A ). AMk h , s s, wh s= s1
h s1. I whw, w h MPE qb hb. N, w
b .
DEFINITION 2 (D Sb S): Sae s is a dynamically stablestate i here exis a iiial sae s0, a se prls {s}s, a mPE sraey
prfle , a t< suh ha al he equilibriu pah we have s= sr all
t.
P , s b h t hs= s
t. O bj () whh b h b b
hz h h s0, () bh hq bw b hz
h .
W whh h hh 0(0, 1) A A. Th h
z h w h.
THEOREM 2 (Chz D Sb S): Suppse haAssupis 1,2,4, a5 hl. the here exiss 0(0, 1) suh ha r all > 0,he llwi is rue.
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1459AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
() Fr ay here exiss a se prls {s}sa a pure-sraeymPE he ae suh ha r ay s0, s
=(s0) r ay 1; hais, he ae reahes (s0) aer e peri a says i his sae hereaer.therere, r eah s0, s =(s0) is a yaially sable sae.
() mrever, r ay se prls {s}shere exiss a pure-sraey mPE.Ay suh mPE has he prpery ha here exiss suh ha r ayiiial sae s0, s
=(s0) r all 1. therere, all yaially sablesaes are axiaially sable.
() I, i aii, Assupi 3 hls, he he mPE is esseially uique: ray se prls {s}s, ay pure-sraey mPE, ay iiial sae s0,a ay , s0
(s0).
P () () Th 2 h h b h b b hz Th 1 -; h A 13 h -MPE h MPE h . A h h hz b
q (5) b b .Th q h Th 1 2 . H b
h-h (), h w b h h h w h w h qb h. Wh
, hw ( > 0), h b h h h h . Cq, w - w h () b Th 1.
Th Th 2 h , b h . F
, w j h - z s. W MPE h
s wh b h . W h
hw h b, h j.C, MPE, w hw h s w
(s), h A 2(i) hw h qb h h -q (s). F,w h (s) A 13.
A b E 1 h I, h bw -
b b w h .
S, P b wh h h b-
w. Th h h whh P
w .
THEOREM 3 (P E): Suppse ha r every w saes x a yhere is a sae z suh ha {wi(z)}i = {wi(y)}i az x, a saeis exeusly sable (i.e.,s r eah s ). the, every (axiaiallyr yaially) sable sae is Pare efie. oherwise, sable saes ay bePare iefie.
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1460 tHE AmERIcAn EconomIc REVIEW JUnE 2012
Th h wh h h h h -
-k h wh
w (whh h b h h xz h h y wh w h ),
P b.
IV. Ordered States and Agents
Th 1 2 hz
b h s0 hA 1 2 . Wh h
hk, A 2 b wh . I h
, w hw h wh h whh - -k-
( h w {s}s ), A 2 . Th b h-w h w .
I b , h h , h wxy b k. Wh h , w k, wh
, b b . S, . G h h h , w
.20 A h w
h .
DEFINITION 3 (S-C S-Pk):give , ,a{wi(s)}i, s, he single-crossing condition hls i r ay i,j a x,y suh ha i wi(x) iplies wj(y) > wj(x) a wj(y) < wj(x)iplies wi(y) < wi(x).
give a{wi(s)}i, s, preerees are single-peaked i r ay i here exiss a saexi suh ha r ayy,z , y < z xi rxi z >y iplieswi(y) wi(z).
W z h h
(.., h j wh h b).
DEFINITION 4 (Q-M V): give a{s}s, player i is aquasi-median voter(i sae s) i r ay X Ws suh ha X= {j : a j b}
r se a,b we have i X.
D h q- s bms. L 1 h Th 4 hw h, h A 1 , h .
20Rh (1990) A-Sh Bk (1999) h , - .A G S (1996) hw, h q - h b wk.
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1461AcEmogLU Et AL .: conStItUtIonS, coALItIonS, And cLUBSVoL. 102 no. 4
DEFINITION 5 (M M V P):give a , hese wii aliis {s}shas monotonic median voter property i r eah
x,y saisyi x
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1462 tHE AmERIcAn EconomIc REVIEW JUnE 2012
W h h b h w b h . F , hh -
h b ,
b. S h k q, w
h b
wi(s) = vi() + V(Z) ,
wh V(Z) , vi() h :
vi() vj() wh i > j.
Th , , h h q ,
{ i}i=1 , (wk) . I , , wh
h q vi() = ( i)2.
S -()j Zh h h ,, h h h bw mZ mZ, wh, b,
mZ h q- . F, h (,Z), whZ b mZ mZ.
Th h hh . G
(., ) w h h- b, b h hh (., ) h h.Th h h h h wh -
h h h b h Zh w h h h . D h, h h
b h hz h
qb.
W bh h A 1 2 , h h
qb h b hz b Th 1
2. T h h , w h wi(s)wi(s) i ss, whh h A 6 h. Th, w (s0) h , bh b, h
s0.
PROPOSITION 1:
() Fr ay eree (super) ajriy,Assupis 1 a2 are saisfe ahus theres 1 a2 apply i his evire. I pariular, here exiss
0< 1 suh ha r ay isu ar > 0, a equilibriu exiss.
()AssueV(Z) be(srily) ireasi(wheeverZZ,ZZ ipliesV(Z) < V(Z )). the r ay iiial saes0, (s0)=s = (Z,)wih Z -aii a leas e he exree players, 1 r.
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T h , w h {s1, ,s| |} h s wk. W h bh h
h, Th 4.21 Th P 1 hw
h wh V , b h
h b h . I, h h b h h h h w h -
. Th, h w b w h
h .
Th h h w b b
. Th h q. I wh w, w h
V(Z) vi() -k i .
PROPOSITION 2:defe A V( ) iV( \{i}) a Ai V( ) V({i}).
() Suppse v1( 1) v1( m) < A a v( ) v( m) < A. the ray iiial saes,Z((s)) = .
() Suppse v1( 1) v1( m) >A1 a v( ) v( m) >A. thereexiss k suh ha i he iiial saes0saisfes|Z(s0) | k, he(i)whe
Z0ilues he ile player(r a leas e he w ile players i is eve),Z((s0)) = , a(ii)wheZ0ilues e he exree players,
Z((s0)) .
()I > 1_
, i.e., he rule is uaiiy, he r ay iiial saes0,Z((s0))= .
Th h hw h
( h w ), h .M , h hw h wh h
, w wh
wh h .
Th h h h , h h
b b h q b h . I, h w w
h h h b
.22 Th h q whh h h
w h
h w -
. Wh h b b , w b h
b w -
b k w h b
21N, hw, h h h h h b ; w k h .
22Th h Th 3, whh hw h wh b h wh h w w , qb P . (R h wh P h ).
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h b h . (O hh w h w
h .)F, w h wh h
h ()j . I , w s = (,Z,), wh, wh [,1] . Th, , h w .
PROPOSITION 3:
()I his evire, Assupis 1 a2 are saisfe a hus theres 1a2 apply.
() Suppse ha ais > 1_ . the r ay equilibriu a r aysaes0,Z((s0)) = .
Th h b h
whh h j -
h. A, wh b , -
. I, h k ( ) , h. W h, hw, h h h
h h h w b. I
, h h I
w h A, h-w h w b b (wh) j h wh k, h b h w b b
q.23 A h , ,
h w b h h
Tk h b h h .
VI. Conclusion
A k , h
h h , b -, j , b h -
bh, h h h
k, b, b h b
h . Th h -
z h h.
W wk h b. W
bh hz b
hw h h () b b .Th hz hhh h s b h
b k w ( s) b . Th h b
23S A, E, S (2008) .
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b P ; h h hh
, b b.
O b h . Sb
, h , h.
Oh, h h , b , hh h h . A b , -
h b h h h b
h b w h , -k
b h b h h .
Appendix
PROOF OF THEOREM 1:
Part 1: W , b , q {1, ,| |}hh
(A1) 1 j < l | | , h l j j.
A 2(i) h , hz h h x,xz z. A h , w b 1.Nw, w h j j k 1, wh k | |. A h h \{ 1, ,k1}, w h h
k (A1) h k.Th , b , : . F k= 1, (k) = k. S w h (j)
j k 1 wh 2 k | |. D h k (4).Th h b whh h b whh - (s) = s kwh k. Ik , h w (k) = k. Ik , h k (k) =zkh h
(A2) s k z sk
( A 2(ii) k, w h h zkh h s kz, h s kz, sk). P 2 k | |, wb q (5).
T h , w h (5) A 13.Th hw A 1 2. I , b , h
(k) = k( h h h ), (k) k.I h ,(k) kk ((k)) = (k) b (4). T hk A 3, - h kh y h hy kk,y = (z), y k(k).Th y kk, b wh (A1), hy { 1, ,k1}, hyk. B h y k(k) (A2). Th h h y , h A 3 .
Part 2: Th q h w: , q
{ 1, ,| |}wh h (A1), (k) (5) k, h
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A 13. S h (k) b (5) k= 1.Th (1) 1, (1) = l l > 1. I h , A 1,b l11 b (A1). Nw, k> 1 b h k whh (k) b (5). S, b , h A 13 h. Th k
(4) w , h k= k. Ik= (k) b (5), h (k) k. Th, A 1 2 (k) kk((k)) = (k). S k= , w h h (k) = l l > k, b h (k) kk (A1). Th h h A 1 A 2 ( bh). Ik, h l= (k). Il > k,h A 1 . Il = k, h A 3 ( h, k
z k b h z kk, z k(k) (z) =z). I l < k, hA 1 A 2 (k)k. Th, (k) b (5), h y kh hy k(k). B h A 3,
y k(k),y
kk, (y) =y . W h b b
.
Part 3: S, b , h 12. Th k:1 k | |h h j1j2 j < k, b h k1 k 2, k 1 k2. Wh , h k1 k 2. Th 2 h 2(k) = l l < k. A A 1 2 2, w b lkk 2(l) = l; h hl2. S, b hh, j1j2 j < k, w h l1.Th, lkk, lk1(k)(b 1(k) = k), 1(l) = l, b h
A 3 1.
Part 4: S A 3 h. S, b , h
s, 1(s) 2(s). P 3 h Th h 1(s) = s 2(s)= s; 1(s) 2(s), w h h 1(s) s2(s). A 1 h 1(s) s s, 2(s) s s, A 3 h h 1(s) s2(s) 2(s)s1(s). Wh , h h h . Th
y = 2(s) h z = 1(s) h hz s y,z s s, 2(z) =z(h hb 1(s) = s b A 2, h 2(s) = s b 3 h Th). Thw A 3 2 s h 2(s) y, .
PROOF OF THEOREM 2:
Part 1: A h w :
(A3) i x,y ,
wi(x) < wi(y) wi(x) < (1 | |)wi + | |wi(y).
T 2, w w h w :
(A4) i x,y,z ,
wi(x) < wi(y) 1 _
(wi(z) (1 ) wi) + wi(x) < wi(y).
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I , h b (A3) (A4). Th, h 0(0, 1) h h > 0, (A3) (A4) h.
Pk s0 S. W MPE h h h h 1, s= (s1). F i s,q ,
(1 )wi(s) s = q(A5) Vi(s,q) = { }(1 ) wi s q
wi((q)) (q) = q+ { }. (1 ) wi+ 2wi((q)) (q) q
I h qb w bw, Vi(s,q) w b h i h s h q. I h , w
.
F h s , k Ks | | 1. Tk s( ) h h A 5 h, (s) s, h s(Ks) = (s). C * w:Eh i Pk(yes) :
() h k= Ks(w h ), PKs = (s) Vi(s,(s)) >Vi(s,s);
() Vi(s,Pk) > Vi(s,(s)).
I , s(k) k, h h Pkb.Th * Mk. W w hw h MPE h .F, w hw h h *, h (s) (s) s
(s) = s. S h (s) s, h A 1 h
Xs {i : wi((s)) > wi(s)} s.
Nw, (A3) > 0 h i Xs, w h
Vi(s,(s)) = (1 ) wi + wi((s)) > (1 )wi(s)
+ (1 ) wi + 2wi((s)) = Vi(s,s) .
Cq, (s) s, h *, h (s) Ks h.
L w hw h h Xs s Pk h h Vi(s,Pk) >Vi(s,(s)) i Xs; .., h wh Vi(s,Pk) > Vi(s,(s)) w s. T b , h h
Xs Pk. Th, Pk s ((s)) = (s), w w h h i Xs, wi((Pk)) > (1 ) wi + wi((Pk)) Vi(s,Pk)
> Vi(s,(s)) (1 ) wi + wi((s)),
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h, b (A3),
wi((Pk)) > wi((s)) i Xs.S,Xs s (Pk) s(s), whh, h (s) s s, (Pk) s sb A 2(ii). B (Pk) s(s), (Pk) s s, ((Pk)) = (Pk) - A 3. Th, h wh Vi(s,Pk) > Vi(s,(s)) w s. Th h *, (s) = s, (s) s, h b h , h PKs = (s) .
S, w h *, - q b (A5). I q s , h h q, wh , h h i
(1 )wi(s). I h , h ( (q)) * (q) q, h h h qb h.H, h b (A5).
Th, w hw h h b * . F -, h h b h h k . F
, h Mk, w b
h h h (wk) , h wh * b. I, (s) s, h h , h i Vi(s,(s)) h Vi(s,s) j. I h , i Vi(s,Pk) Pk
Vi(s,(s)) j (b (s) w b (s) s (s) = s). Th, h -b * h (A1). Th, * b s , h * MPE h .
Part 2: W h MPE , h h MPE h h . W A 13. Tk q { 1, ,| |} (A1). Th, w h b Th 1. F, w (1) = 1. I l 2 w h l= , h (l) = l;
hw, Zl lb
Zl = {z l : s l : s z s l z}.
Th Zl, w A 2(b) l. Ch - Zl (l) w. L Yl b h l h h j Yl, l(j) l(j) Zl, l h z Zl: wi(z) > wi(l), wh i = l(j). B A 5, Yl ; kl
* b h Yl. Il(kl*) , h (l) = l(kl*), whl(kl
*) , h (l) b z Zl h h wi(z) > wi(l) i = l(j ). P b l, w .
W w qb h . I h qb, - i h s q , Vi(s,q), b (A5); , h i Vi(s,s). G
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h , h b w () wh b Vi(s,q). W MPE h b bkw .
Case (i):(s) s. G s, h ks* b h . Iks* h , h Ksw ks*+ 1 w h w. S h h , h h s. C h 1, w h SPE,s b s = (s) j hw. B b Ys, s b b i. P bkw h - , w h h i h wi((s)) wi(s), h h s, whh h s = (s) h b . B (s) h h h Ksh h h s. W h
ks*+ 1, SPE h b ks*+ 1 wh s .
C w ks*. B h , (s) b . A h , h h h
, s(ks*) = i , h i b (s): i , hs . H, b h ks*, h SPE wh (s) .
I ks* 1, w wh bkw . A ks* 1, h h (s) b , w h h h (s)
j h ( ks*
). I h h - i, h , w k . P bk-w, w h SPE h h s h (s) s.
Case (ii):(s) = s. Tk h , h s s . F i s, wi((s )) > wi(s) h. S(s) = s, hw, h w . Cq,w h h h w b -
. Cq, h - , b h,
h b . W bkw wh .
N h bh , w h b Mk b h h q b wh . H
s , w Mk . B h h -, h b (A5), h- h b -h (hw, w b SPE s). Th hw h MPE.
O bh h h MPE . Tk
{s( )}s - MPE . F s, h qh h qb h w- ( q = s - j) (s) = q. F, h : h :(s) s h > 1, (s) s(wh 2(s) ((s)), .). Th b bh b . S h h h (s) = s, b
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(s) s. D bJs {1, ,Ks}h s wh - Pk h qb h . B , h Js (s). Tw b.
Case (i): k Js, +1(Pk)(Pk) . Th h - k Js. IPk , h i wi, Pk j, i (1 )wi(s) + wi> wi. B Pk b MPE, h .
Case (ii): k Js, +1(Pk) =
(Pk) . D h h kbJsJs; , h Js Js. L kb h Js; h+1(Pk) =
(Pk) | | 1. C h kJsh k. A h k, Pk, wi h i, wh j (1 | |) wi+
| |wi(| |(Pk)) > wi. Th, Pk
b MPE, whh bh h
.
Th h (s) = | |1(s) | | 1.D (s) = | | 1(s), , wh h h 0(s) s,
(A6) (s) = { {0} : (s) = (s)}.
E, 0 (s) | | 1, (s) = 0 (s) = (s) = s.
M,
(A7) ((s)) = ((s)) = ((s)) = (s)
s, w h . F,
(1 )wi(s) (s) = s(A8)
_
Vi(s) = { } + wi((s)),(1 ) wi (s) swhh h qb i h qb (s) , , h b h ,
_
Vi,
(1 )wi(s) s = q(A9)
_
Vi(s,q) = { }+ _Vi(q) .(1 ) wi s qC,
_
Vi(s,q) h i s q , qb ( ) w. W w ; h w w h (s) A 1 2, h h (s) = (s)(whh s= (s0) 1), h A 3.
Pr ha i prpsals Pkj a Pkl, j < l, are prpse a aepe i sae s,he (Pkj) (Pkl)a (Pkj) (Pkl). W h wh(s) s, h, (s) 1. F h s k h Jh
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h h kJ, h Pk . LJ= {k1, ,k|J|}, wh kj< klj < l(w s ); hJ. I qb, Pk1 , (s) = Pk1 (Pk1) = (s). S h Pkl 1 l |J| h qb, h 1 l < |J|,
_
Vi(s,Pkl) _
Vi(s,Pkl+1) w
s. F h ,
(A10) (1 (Pkl)+1) wi + (Pkl)+1wi((Pkl))
(1 (Pkl+1)+1) wi + (Pkl+1)+1wi((Pkl+1)),
h, (A3), wi((Pkl)) wi((Pkl+1)); h (Pkl) s(Pkl+1). W h h
_
Vi(s,Pk|J|) _
Vi(s,s) w s, h ,
(A11) (1 (Pk|J|)+1)wi + (Pk|J|)+1wi((Pk|J|))
(1 )wi(s) + ((1 (s))wi + (s)wi((s)))
> (1 (s)+1) wi + (s)+1wi((s)).
F (A3), w wi((Pk|J|)) wi((s)) = wi(Pk1); h, (Pk|J|) s(Pk1).
A 2(ii) w h (Pkj) (Pkl) 1 jwi(s). W h h h s h h (s) s, (s) s s, h A 1 h.
Pr hasaisfes Axi 2 hw ((s)) = (s) (A7).Pr ha(s) = (s). I(s) = s, h (s) = s = (s) h
. L h (s) s, h (s) k ; .., h (s)= (s)(, q, (A6)(s) = 1 wh (s) s).C w .
Case (i): (s) = Pkj j : 1 j |J|. I h , (Pkj) = 0 A 2 h. B w h (Pkl) wk l,h, ((s)) = (Pk1) = 0, h (s) = 1.
Case (ii):(s) = Pkj h j. Th h (Pk1) 1 (s) (s). S h k, h Pk= (s) ( h qb h). Th , h i w _
Vi(s,Pk) = (1 ) wi+ wi((s)), j, h w
_
Vi(s,x) (1 )wi(s) + (1 ) wi + 2wi((s))
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xh h (x) = (s). A wh wi((s)) > wi(s) , (A3), h
_
Vi(s,Pk) >_
Vi(s,x). S (s) s s(A 1), Pk= (s) wb .
B A 5, h w b
k, h w b -. I h , k J, b h (s) = Pkj h j, . Ih , i h h wi((s)) > wi(s) h - k, h h Pk= (s) qb, w b , w . P Pk= (s), hw, w _
Vi(s,Pk) wh k h qb w _
Vi(s,x). F i,_
Vi(s,Pk) >_
Vi(s,x) w , h h h b . Th h qb, whh h (s) = (s) s .
Pr hasaisfes Axi 3. S h A 3 h. Th h h s,z h h (z) =z,z s s(whh z s),
z s(s)(whh (z) (s)). A b, h k, h Pk=z ( qb h). I , h i w
_
Vi(s,z) = (1 ) wi+ wi(z), j, h w
_
Vi(s,x) (1 )wi(s) + (1 ) wi + 2wi((s))
xh h (x) = (s). Nw, (A4) h_
Vi(s,z) >_
Vi(s,x) wh- wi(z) > wi((s)); .., w s. Th, Pk= zw b .
S (z) (s), b hz h qb h.B A 5, h b h b h - k. Wh wh wi(z) > wi((s)) b h -,z b h. Th h qb,
h bh h A 3. Th h 2 h Th.
Part 3: Th w Th 1 2 h
Th.
PROOF OF THEOREM 3:S, b , h b s P .
Th h x, wi(x) > wi(s) i . B hh, hy h h y s wi(y) = wi(x) > wi(s) i . Tk - . h A 13. C w . I(y) =y, h (s) = s y s s w y s(s), A 3 ( h z h h(y) =y, y s s, y s z, h z (s)). I (y)y, h A 1 wi((y)) > wi(y) > wi(s) w y, whh w s, h (y) s s (y) s(s). A 2 h ((y)) = (y).A, w h A 3.
PROOF OF THEOREM 4:
Th , h A, hz q-
. R hms h q- s.
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LEMMA 1: give , , pay uis {wi(s)}i, s, a wiialiis {s}ssaisyi Assupi 1, he llwi are rue.
() Fr eahs, he sems is epy.
()I he sile-rssi prpery i defii 3 hls, he r ay saesx,y,z ,
xz yi a ly i r alli mz, wi(x) >wi(y), a
xz yi a ly i r alli mz, wi(x) >wi(y).
()I i eia ver ii i defii 5 hls, he here is aereasi sequee{s}s players suh hasmsr alls .
PROOF OF THEOREM 4:
Part 1: W wh A 2(i). S h h s1, ,slh h sk+1sksk 1 k l 1 s1slsl. Tk q {s}s. R h s w s, h, x z,xz z, h wx(z) > wz(z). Nw hs w wh s h ;.., s= {X : s X}. D h bw b, w h h xz z, hxz
z. Cq, h w s1, ,slh h sk+1sksk 1 k l 1 s1slsl, h w h sk+1 sk sk
1 k l 1 s1 sl sl; h, . Nw k h h (whh b ). Wh , h s2 h w ( s2 s1 s2 s3); h s2 s1 s2 s3.S s3 s2 s2 s2 s1 s1, w h ws2(s3) > ws2(s2) ws1(s2) > ws1(s1).B s2 s3 s2 s1, h, ws2(s3) ws2(s2) > 0 ws1(s3) ws1(s2) > 0. Cb h wh ws1(s2) > ws1(s1), w h ws1(s3) >ws1(s1). B h s3 s1 s1, s1 h s1. Th h s2 b k h , h h {sk}k=1
l h h.
T A 2(ii), k s s ms. S h s1, ,slh h sk+1s sk 1 k l 1, s1s sl, sj sk1 j < k l. Wh , h slz h - s s1, ,sl. Th ws(sl) ws(s1), A 6 ws(sl) > ws(s1). B h, b L 1, s1s sl, h h - . F, x,y h h xs s y s x, h i ms w h wi(y) > wi(x) > wi(s), whh, , y s s. Th hwh A 2(ii) h h 1.24
24Th b Th 4.6 A-Sh Bk (1999).
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Part 2:25 L = ss; h , w , - A 1. L * b b x*y {i : wi(x) >wi(y)} . S -k, Th 4.1 A-Sh Bk (1999) h * , h . C,
A 2(i) w b *; A 6, w A 2(ii). H, h . F, Th 4.1 A-Sh Bk (1999) h h s -, xs s y s xy s s.
Prs Prpsiis i Sei V
PROOF OF PROPOSITION 1:
Part 1:S > 1_2
h , A 1 . E s1, , s(wh = | |) h h sk wk k(h wh h b b). Wh h , h- D 3. I, sk< sl i < j, h
(wj(sl) wj(sk)) (wi(sl) wi(sk))
= (vj(sl) vj(sk)) (vi(sl) vi(sk)) 0,
b sk sl v h . Nw q q- ; h w
h h. F sk, k sk h hsk sk < sk+1 sk < , sk = hw. Th sk q h sk, wk , q- skbh b . W w 1 Th 4 hw h A 2 Th 1 Th 2 .
Part 2: S h s wh 1, Z(s) b. SZ(s) = [a,b]
Z = [a 1,b + 1]. Th mZ mZ mZ mZ, h s = (s,Z ) b . B h V(Z), sP - s. Tk h A 13 x= (s ). ThA 1 h wi((s )) wi(s ) > wi(s) w s, h, b L 1, i ms . Th, h h i ms, h w s. S ((s )) = (s ), w A 3. Th h s b, h 1 h b Z(s) b s. H, s0, h wb .
25W hk h 2 Th 4.
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PROOF OF PROPOSITION 2:
Part 1: N h xwhZ(x) = b, wh (x)xw A 1. I, m x m
-k, q- mw b w y why > x, mw b w y < x. Nw , b , h s h hZ(s), (s) = s. C h w. C (): (s) < m. Tkx= ( m, ); b hh, w1(x) > w1(s), h
w1(x) = v1( m) + V( ) > v1( 1) + V(s) v1(s) + V(s) = wi(s) .
S (x) > (s), h wi(x) > wi(s) i . B w h xb, h (s) = s A 3. C (): m s m. Tk
x= (s, ) h wi(x) > wi(s) i . S w h(x) =x, w A 3. C (): s > m.Th (). I , (s) = s .
Part 2: L k= 1. L s b h hZ(s) kZ(s) h . D h Z(s) b i k x= ( i, ), whh b . Th (x) =x . I(s) x, h A 3 , wi(x) > wi(y) y x. Th h (s) =x.
I s h 1 Z(s) k, h h s = (
1,{1}) s = ( ,{}). S h (s) =x= (, ); h m m, v1() v1( m) v() v1( m) b -k. Th h ,
w1(x) = v1() + V( ) v1( m) + V( ) < v1( 1) + V({1}) = w1(s) ,
h A 1 . S, h ,w(x) < w1(s), A 1 . Th h (s) x.
Part 3: Tk s; , b , h (s) =xh h
Z(x). B A 1, wi(x) > wi(s) i . Cy = (x,); h - hy b (x). A hw , (y) =y, wi(y) > wi(x) > wi(s) i . B h (s) =x A 3, .
PROOF OF PROPOSITION 3:
Part 1:Th w h 1 P 1.
Part 2: S, b , h s, (s) =xh hZ(x) h A 1 3. B A 1,wi(x) > wi(s) w s. Cy = (,x, ) h h >
1_
; hy -b. B (y) =y, wi(y) > wi(x) i . Th wi(y) > wi(s) w x. B h (s) =x A 3, .
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REFERENCES
Acemoglu, Daron, Georgy Egorov, and Konstantin Sonin. 2008. C F N-D-.Review Ei Suies 75 (4): 9871009.
Acemoglu, Daron, Georgy Egorov, and Konstantin Sonin. 2009. Eqb R D
V G. Mh I Th D E Wk P09-26.
Acemoglu, Daron, and James Robinson. 2000. Wh D h W E h Fh? D,Iq, Gwh H P. Quarerly Jural Eis 115 (4): 116799.
Acemoglu, Daron, and James Robinson. 2006. Ei oriis diarship a deray.Nw Yk: Cb U P.
Alesina, Alberto, Ignazio Angeloni, and Federico Etro. 2005. I U.Aeria E-i Review 95 (3): 60215.
Austen-Smith, David, and Jeffrey S. Banks. 1999. Psiive Pliial thery I: clleive Preeree.A Ab, MI: U Mh P.
Barber, Salvador, and Matthew O. Jackson. 2004. Ch Hw Ch: S-Sb MjR C. Quarerly Jural Eis 199 (3): 101148.
Barber, Salvador, Michael Maschler, and Jonathan Shalev. 2001. V V: A M hE E. gaes a Ei Behavir37 (1): 4078.Barber, Salvador, Hugo Sonnenschein, and Lin Zhou. 1991. V b C.Eeria
59 (3): 595609.Bordignon, Massimo, and Sandro Brusco. 2006. O Eh C.Jural Publi E-
is 90 (1011): 206390.Bourguignon, Franois, and Thierry Verdier. 2000. Oh, D, Iq Gwh.
Jural develpe Eis 62 (2): 285313.Burkart, Mike, and Klaus Wallner. 2000. Cb E: E L A. h://
./b=248994.Chwe, Michael S. Y. 1994. Fh C Sb.Jural Ei thery 63: 299325.Ellickson, Bryan, Birgit Grodal, Suzanne Scotchmer, and William R. Zame. 1999. Cb h M-
k.Eeria 67 (5): 11851217.
Gans, Joshua, and Michael Smart. 1996. Mj V wh S-C P.Jural Publi Eis 59 (2): 21937.
Gomes, Armando, and Philippe Jehiel. 2005. D P S E I-: O h P I.Jural Pliial Ey 113 (3): 62667.
Jehiel, Philippe, and Suzanne Scotchmer. 2001. C R E J F-.Review Ei Suies 68: 393413.
Konishi, Hideo, and Debraj Ray. 2003. C F D P.Jural E-i thery 110 (1): 141.
Lagunoff, Roger. 2009. Th D Sb R P I. gaes a E-i Behavir67: 56983.
Lizzeri, Alessandro, and Nicola Persico. 2004. Wh D h E E h S? D h S G, wh A B A R. Quarerly Jural Eis 119 (2): 70563.
Mariotti, Marco. 1997. A M A S F G.Jural Ei the-ry 74 (1): 196217.
Rabasa, Angel, and Stephen Larrabee. 2008. the Rise Pliial Isla i turkey. S M, CA:RAND.
Ray, Debraj, and Rajiv Vohra. 1997. Eqb B A.Jural Ei thery73 (1): 3078.
Ray, Debraj, and Rajiv Vohra. 1999. A Th E C S. gaes a E-i Behavir26 (2): 286336.
Roberts, Kevin W. S. 1999. D V Cb. h://./b=1160966.Rothstein, Paul. 1990. O R P Mj R. Sial chie a Welare
7 (4): 33142.Roy, Olivier. 2007. Seularis crs Isla. Nw Yk: Cb U P.
Schauer, Frederick. 1985. S S.Harvar Law Review 99 (2): 36183.Scotchmer, Suzanne. 2002. L Pb G Cb. IHabk Publi Eis,
b A Abh M F, 19972042. A: Nh-H.
http://ssrn.com/abstract=248994http://ssrn.com/abstract=248994http://ssrn.com/abstract=248994http://ssrn.com/abstract=248994http://ssrn.com/abstract=248994http://ssrn.com/abstract=1160966http://ssrn.com/abstract=1160966http://ssrn.com/abstract=1160966http://ssrn.com/abstract=1160966http://ssrn.com/abstract=248994http://ssrn.com/abstract=248994