Jul 26, 2001 - ")(0 %21435 3 6478#&%27894@B A87C%&3EDGFH%2I4D23P "$9Q %&DGF)RS7894@U TSD2")V£AC3XW # F)9SF)ACYa`E3X#' %21435 ...
Dependence in Private Values and Efficiency in Bilateral Trade. Georgia Kosmopoulou University of Oklahoma
Abstract In a bargaining model with dependent private information, I extend the result on existence of efficient mechanisms allowing any distribution of the surplus among traders. This generalization introduces flexibility into the model since full surplus extraction by one trader is incompatible with ex post individual rationality.
I would like to thank an associate editor of this Journal for helpful comments. Citation: Kosmopoulou, Georgia, (2001) "Dependence in Private Values and Efficiency in Bilateral Trade.." Economics Bulletin, Vol. 3, No. 9 pp. 1−7 Submitted: July 26, 2001. Accepted: August 15, 2001. URL: http://www.economicsbulletin.com/2001/volume3/EB−01C70008A.pdf
"!#!$"%& %&'"(*)&%+!-,/.0 1", !2'3,/.45%&'"(765, 8)+!:9 .'5.)+;=?%+!-K!:4 .H!$?65, !: %&'"(L "!M8I!:)&%+!-N I.0(!:'O -@HPQ"!:'# "!M8I!:)&%+!-N .0, !#%&'54"!-6I!:'54"!:'OFR.'O;65,/%+>0.0!:)+;78!-, >!:43 %+('5.)AE "!2.0(!:'O -ST,/.0!-(%&G8I!:5.:>?%+,)+!:.45UV;=6%&G-.)&)+;* )+ !:H%&'!WXG-%+!:'5G;@YPQ%+ #4"!-6I!:'54"!:'O 8I!:)&%+!-N-E"ZK!->!-,:E"[,?:\! 9#!-,R.'542]G-^T!:.']_C`:abc=E`:abbdH.'542]G-eUf!-! .'54hgF!:'O;i_C`:aajd "ZK!:4h 5.0k%+k%&6I %+8)+!!:)&%&9 %&'5.0!2 "!l%&'"!WXG-%+!:'5G-%+!:. ?G-%&.0!:4hKU%+ D65,/%+>0.0! %&'"f,/9 .0 %+'@BC'm "!:%+,U!- %&'"("E "!kG'545%+ %+'5.)T45%&,/%+81" %+'XH65,/%+>0.0!k%&'"f,/9 .0 %+'*>0.0,/%+!:-EG, !:.0 %&'"(X. 45%+>!-,/ %+V;L?8I!:)&%+!-N.G, nV;=6I!:-@ oF5%&T45%+>!-,/ %+V;L?8I!:)&%+!-NI(%+>!:n.'656I, 15'5%+V;LUG'5,/15G .0, 8%+,/.0,/%&)+; )&.0, (!*6I!:'5.)+ %+!:#.'54p, !-KJ.0,/45_f6I %+ %+>!m.'54p'"!-(.0 %+>!,/.'5f!-, 6.:;?9#!:'O qdr4"!-!-,l "!.0(!:'O f, 9 9 %&, !-65, !:!:'O %&'"(2 "!:%+,M65, !-f!-, !:'5G!:-@ oF"!:! , !: 15)+ K!-, ! !: .08)&%& "!:43%&'h.'r.15G %+'hf,/.9#!-K, sE 8=;D%&9#6I %&'"(7 "! , !:,/%&G %+'3 5.0k "! !:)&)+!-,M!$?,/.G U.)&)8I!:'"!t Jf, 9u,/.4"!'*.:>!-,/.0(!@Mvw>!:'* "1"(7 5%&J, !:,/%&G %+'*9 .:;X8I!4"!: %+,/.08)+!%&' .15G %+'5-EI%+L%&L.0, %xtG-%&.)n%&' %+ 15.0 %+'5FKU"!-, !k "!2.G/5%+!->!:9#!:'Ow!WXG-%+!:'5G;%&F "!29 .Zy,G'5G!-,/'@LeL .']!$".9#6)+!G'5 %&4"!-,L "!2G-.!2wVK*45%+>?%& %+'5JR.l815 %&'"!: U15'5%+U%&'O>)+>!:4D%&'%&'O!-,/'5.)n,/.'5 .G %+'5-@ oF"!LG9#6.'O;S J9 .%&'l%&'O!-, !:J%&R'"J"ZKz "!L 1", 6)&15w%&R45%&,/%+81"!:4#8I!-VK!-!:'X "!L45%+>?%& %+'5Y81"R,/.0 "!-, KU"!- "!-, "!21" G9#!#%&L!WXG-%+!:'O,'"-@BC'N.G-ETBU "ZK{"!-, !E 5.0 "!, !:|=15%+, !:9#!:'OLRN15)&)n 1", 6)&15 !$?,/.G %+']8=;* "!!:)&)+!-,L%&U'"L'5)+;7, !:,/%&G %+>!k81"U%&'5G'5 %&!:'OFKU%+ m!$6IU%&'545%+>?%&4515.),/.0 %+'5.)&%+V;@ oF5%<'545%&'"(}%&*.)&) "!h9#, !r%&9#6I, .'O* %&'5G!39 .'O;Q,/.45%&'"(p9#!:G/5.'5%& 9 *%&'5G-)&1545%&'"(~.15G %+'5m.0, ! !I!:G %+>!:)+;7!$*6IF%&'545%+>?%&4515.)&)+;,/.0 %+'5.)A@ BC'l)&%+(Ow 5%&w, !: 15)+-EBH65, ?G!-!:4 2.'5.)+;=!:4EO "!U.0(!:'O 5.:>!.65, 8.08%&)&%+V;k45%&,/%+81" %+'/* . Z>!-, "!X!:)+!:9#!:'O k %!0 @]oF5%&6.06I!-,2G'5 %&4"!-,/k.65,/%+>0.0!l>0.)&1"!l9#?4"!:)RKU%+ r4"!-6I!:'54"!:'O8I!:)&%+!-Nk.'54 , !:,/%&G F.0!:'O %+'ml!WXG-%+!:'OF45%+, !:GM, !->!:)&.0 %+'9#!:G/5.'5%& 9 -@ ^T!-214-3 _$
('"$Z# d8I!l "!X6.:;?9#!:'OM "!X81";!-,:E517Z6 _$
*'"$# d "!X, !:G!:%+65kF "!7!:)&)+!-,.'54~)+!-9Y 8 _$
*'"$# d >0.)&1"!:]%&' "!}!-
4"!:'"!J "!J65, 8.08%&)&%+V; 5.0Y "!J8?y!:Gw%& ,/.'5f!-, , !:4k "!J81";!-,YKU"!:' "!J, !-6I, !:4>0.)&15.0 %+' "!
:
I.'54;"$#J, !:6I!:G %+>!:)+;*_f!WXG-%+!:'5G;2, !:|=15%+, !:48Y_$
?%&4515.)&)+;,/.0 %+'5.)AEn_fB BCgd %+nf,F!->!-, ;b"$ # %&' % O T WVX .w_$
R "$# dYG 8Y_$
*'"$# d!-, ;D%&'545%+>?%&4515.)IKU%&)&)n>)&15'O .0,/%&)+;m6.0, %&G-%+6.0!#%&'] "!#9#!:G/5.'5%& 9 %&9#!"!s?'"ZKUU5%&65,/%+>0.0!%&'"f,/9 .0 %+'@
L,},Fd
oF"!F9#!:G/5.'5%& 9 %&H!$*.'O!k8154"(!-M8.)&.'5G!:4En_NvRe
.0 "!
%+'l.:>!-,/.0(! "!F6.:;?9#!:'O RI "!F81";!-,w!:|=15.)
"!, !:G!:%+65 M "!k!:)&)+!-,:E"%A@ !@+E
T #K) XV .w_Q"$# d T WVX .w_$
R "$# d!]G9#6.0 %+8%&)&%+V;
rO T 6 .w_$
R "$# dYG 143:_$
*'"(c dCZ^8Y_$
*'"(cd?%&4515.)",/.0 %+'5.)&%+V;7G'545%+ %+'*%&9#6)&%+!: 5.0
8Y_$
*'"(cd!kG9#6.0 %+8%&)&%+V;lG'545%+ %+'*)+!:.45M "!f)&)+ZKU%&'"(#G'545%+ %+'rO T 6 w. _$
R "$# dYG Y8 _$
*'"(c d!-, ;2%&'5 .'5G!
f, 9,/.4"!F'#.:>!-,/.0(!#_NvRe
,},
_Nv
9#!:G/5.'5%& 9Xd/@"!$#&%$#&'#
(
oF"!-, !:9 jJ65, Z>?%&4"!: "!R 1?WXG-%+!:'OTG'545%+ %+'5I' "!R.0(!:'O -SZ8I!:)&%+!-NIf,n!$"%&!:'5G!w".'!WXG-%+!:'O-E B [LE
L,},~9#!:G/5.'5%& 9.)&)+ZKU%&'"(U "!J6I %+8%&)&%+V;L 5.0Y "!J(.%&'5 f, 9
B BCgp.'542vRe
,/.4"!M9 %+(O 8I!J 5.0, !:48=;k "!
.0(!:'O -@LoF"!:!G'545%+ %+'5M, !:|=15%+, ! 5.0U "!k>!:G,wG'545%+ %+'5.)65, 8.08%&)&%+ %+!:MG, , !:6I'545%&'"(#7.'O; >0.)&1"!H.#,/.4"!-,:S FV;=6I!kG-.''"F8I!!$?65, !: !:4m.U.l)&%&'"!:.0,FG9k8%&'5.0 %+'*Y "!>!:G,/LG, , !:6I'545%&'"( 5%& "!-,V;=6I!:-EnKU%+ 3'"'5'"!-(.0 %+>! K!:%+(O6)&.G!:431"6I'D "!:9*@ oF"!-;D.0, !l 1?WXG-%+!:'OG'545%+ %+'5 G, !:.0!D!:'"1"(z, =9
f,*9#!:G/5.'5%& 9 8.!:4z'6I!:'5.)+ %+!:X.'54, !-KJ.0,/45l}4"!-!-,7 "!],/.4"!-,/lf, 9
9 %&, !-6I, %&'"(X "!:%+,>0.)&1"!:-@ oF"!#65, =RJ "!-, !:9
j*%&8.!:43' 5.0, s0.-Sn)+!:9 9 .?@#B (!:'"!-,/.)&%+!:9#!:'OMn!WXG-%+!:'5G;l%& "!U65,/%&9 .0, ;2(.)%&' "!L4"!: %+(' n9#!:G/5.'5%& 9 -E=.'O; 45%&,/%+81" %+'2 "!L 1", 6)&15Y 5.0J)+!:.45Rk!WXG-%+!:'O 1" G9#!:U "15)&478I!G'5 %&4"!-, !:4@
O
7,
MeL'm!WXG-%+!:'O-E J.:;!: %&.']%&'5G!:'O %+>!G9#6.0 %+8)+!E%&'O!-,/%&9
*O
.'O!8154"(!-F8.)&.'5G!:4*9#!:G/5.'5%& 9u!$"%& F%+ _C`ZdJ "!-, !4"=!:F'"F!$"%&F.
"(c\F %
` Q"$# &X"$#F %
.'54*.#N.9 %&)+; n_ d
%&'545%+>?%&4515.)&)+;2,/.0 %+'5.)n.'54m!$
O
15G/* 5.0
Q"$# dgAe"$#EF % .'54 _f8Id}.w_$
R "(cdS T V n_Q"$#Zd*.w_$
R "$# dRf,U.)&)C
F u.'54 _AjdJ "!-, !4"=!:F'"F!$"%&F.'e frF } .'54m.#N.9 %&)+;` R_$
d&
5F 15G/* 5.0O _N.Od R_$
ddg A
F .'54 _f8Id}w . _Q"$# R ff d= T 6 Vr 6 R_$
d*w. _Q"$# R
dlf,L.)&)7"$#?F % KM O B Y "!G'545%+ %+'5MwoF"!-, !:9 j ")&4E5'"!G-.']G'5 %&4"!-,U.#t5$?!:4 5.0,/%&'"( ,/15)+! 5.0L .0 %&Ct!: _N.Odn_ Zd
%&'545%+>?%&4515.)5,/.0 %+'5.)&%+V;7.'54m%&'O, ?4515G!4"!->?%&.0 %+'5Mf, 9u 5.0F,/15)+! 5.0U5.:>!k0.)&1"!KU"!:' "!l.0(!:'O k, !-6I, ,/1" "N15)&)+;.'54h6I!:'5.)&%+!l!$?6I!:G!:4r,/.'5f!-,/
KU"!:'7 "!-;*9 %&, !-6I, -@
.>!:G, ) KU%+ 7!:)+!:9#!:'O _$
('"$#Zd F KU"!-, !E"$#?F % E"f,UKU5%&G/rO T .w_Q"$# R
d _$
*'"$# d>g A .'54 T .w_Q"$# R ffd _$
*'"$# dgAI ^ f
!-, ;].0(!:'O915L8I!6.%&4m'] "!#9 .0, (%&' "!2 1", 6)&15 (!:'"!-,/.0!:4p8=;~5%&65,/%+>0.0!*%&'"f,/9 .0 %+'~%&'~,/4"!-,#h%&'54515G!X5%&9
3, !->!:.)JKU5.0 "!7s?'"ZKU265,/%+>0.0!:)+;@
oF"! 1"645.0!:4345%&,/%+81" %+'mJ "!#656I'"!:'O -SV;=6I!:k%& "! .9#!lG'545%+ %+'5.)Y'h.'O;DV;=6I!#65,/%+>0.0! %&'"f,/9 .0 %+'@eL.X, !: 15)+-E'"X6.:;?9#!:'O G/"!:9#!#G-.'3"!:)+6345%xI!-, !:'O %&.0! "!2!$?6I!:G!:4D6.:;?9#!:'O 9 .4"!
8=;3.0(!:'O KU"9 %&, !-6I, .'54h "!lKU"4"'S -@ '5G! "!X1"645.0!:4h45%&,/%+81" %+']45%xI!-,/4"!-6I!:'545%&'"( ' "!65,/%+>0.0!%&'"f,/9 .0 %+'*Y!:.G/D.0(!:'O-EI'"!G-.']%&'O, ?4515G!6.:;?9#!:'O U 5.0L%&9#6I!k)&.0, (!6I!:'5.)+ %+!: KU"!:'~9#!-'"!7%&9 %&, !-65, !:!:'O %&'"(5%&k65, !-f!-, !:'5G!:.'54r, !-KJ.0,/45KU"!:'r"!7%&k!:)&)&%&'"(m "!X,/1" @]oF"! 4"!: %+('"!-,MG-.'* "!:'7.4 y 15J "! %+!.'54*'"!-(.0 %+>!,/.'5f!-,M6.:;?9#!:'O M#, !:,/%&GJ "! 1", 6)&15 5.0U%&M.06565, 65,/%&.0!:478=;7!:.G/.0(!:'O-@ eLU%&U4"!:9#'5,/.0!:4m8I!:)+ZKE"ZK!->!-,:E "!k9#!:G/5.'5%& 9 M65, 6I!:4m%&'* "!-, !:9
j#G-.'5'"U8I!!$*6I
8154"(!-M8.)&.'5G!:4@RBC'm.'*!$*6IF8154"(!-M8.)&.'5G!:4m9#!:G/5.'5%& 9u "!k4"!->?%&.0 %+'5Mf, 9u "!t5$?!:4m 5.0,/%&'"(
a# Q"$# ]# $
*'"$# d _$
d _$
*'"$# d
,/15)+!U "15)&4#8I!U "!L .9#!Lf,8I ,/.4"!-,/-E=f,J.'O;#6.%+,RV;=6I!:-E"%A@ !@+E _ d O_ c
Y_$
('"$#Zd/@MBC'm 5%&UG-.!Y_$
*'"$# dM "15)&4* .0 %&f;Ef,L.)&)
VEr f
E "$#0EI.'54`"(c "$#0E "!kf)&)+ZKU%&'"( !- HG'545%+ %+'5O w. _$
R "(c dY_$
('"$Z# d >gAI .w_Q"$# R
dY_$
('"$# dSBAI _C`Zd # w. _$
R "$# dY_$
*'"$# d=BAI w. _Q"$# R
dY_$ f['"$Z# d DgAI _Ajd # oF"!G'545%+ %+'5M%&'h_HjdM%&9#6)+;4O T # w. _Q"$#a
dY_$ f['"$# dDgA T # w. _$
R "$# d*w. _Q"$# dY_$ f['"$Z# d DgA T T # w. _$
R "$# d*w. _Q"$# dY_$ f['"$Z# d DgA T # w. _Q"$# d T w. _$
R "$Z# dY_$ f['"$# dDgA T # w. _Q"$# dY_$ f['"$#Zd DgAI , !-Z>!-,:EIG9k8%&'5%&'"(2 "!G'545%+ %+'5M%&'h_M`Zd, !: 15)+ M%&'rO T w. _$
R "(c dY_$
('"$Z# d >gA T # w. _Q"$# d T w. _$
R "(0c dY_$
('"$# d>gA T w. _$
R "(c d T # w. _Q"$# dY_$
*'"$# d >gAI ?%&'5G! T # w . _Q"$# dY_$
('"$Z# d DgA r
?%&.0 %+'5Jf, 9u "!t5$?!:4* 5.0,/%&'"(2,/15)+!%&9#6I!6I!:'5.)+ %+!:J.0U "!%&'O!-,/%&9u .0(!k!->!-, ;7 %&9#!.'
.0(!:'Ok9 %&, !-6I, L5%&LV;=6I!@oF5%&-EI"ZK!->!-,:E %&'".7G/5.0,/.G!-,/%& %&G2 5.0%&'"!:G!: .0, ;J9#!:G/5.'5%& 9 5.0l%&'54515G!*,/1" O!:)&)&%&'"("@}B l%I %+8)+!X 5.0-EJf,X9#!m, !:.)&%+?%+15M.0, (159#!:'OF4"=!:F'"M65, Z>!k'"'"!$"%&!:'5G! !$76IM8154"(!-M8.)&.'5G!:4 9#!:G/5.'5%& 9 -EY%&'3(!:'"!-,/.)A@7B 9#!-, !:)+;D6I%&'O ] "!lN.Gk 5.0%+k%&k'"k6I %+8)+!2]G'5,/15Gk!$h6I 8154"(!- 8.)&.'5G!:429#!:G/5.'5%& 9 5.0Y6I!:'5.)&%+?%&.0 %+'kf, 9 ,/1" O!:)&)&%&'"("@
w S w
L65 %&9 .)==!:)&)&%&'"(`=,/.0!-(%+!:L'54"!-,L'5G!-, .%&'OV;Df,.%& G,/%&9 %&'5.0 %&'"(2'"6I)&%&JPQ"!:'L!:9 .'545FeU, !BC'54"!-6I!:'54"!:'O % !#"$&% E ( 6Oc (' `0@ [,?:\! 9#!-,:E( "@+E.'54m]G-^T!:.'Eg@ @+E _C`:abbd 515)&)TvH$?,/.G %+'mY "!2?1", 6)&15J%&'^,J.:;!: %&.'].'54)L 9 %&'5.'O =,/.0!-(;*eL15G %+'5 % !#"*$& + En`:j 6-, /`:jcb=@ .155'0/k@0P @+E .'542o 15G s!-,wek@0P @+E_C`:ac?`Zd2134(" 54(6879";:?"A"@ BC:D"E@>CFG>CE0q> E w,/%&'5G!-'*L '5%+>!-,/ %+V; [,?:\! 9#!-,:E "@+En.'54h]G-^T!:.'Eng@ @+EJ_C`:abcd
w, !: -@
'
& !#"
]G-eUf!-!E?g@ @+E .'54 gF!:'O;E @+EI_C`:aajd /[, , !:)&.0!:4#BC'"f,/9 .0 %+'2.'54#!:G/5.'5%& 9 L!: %+(' "%
+ E ( ac 6Oj?`0@
"**4E]G L,/.:K E/L%&)&)AE U!-K w, s@ ;!-,/'Eg@+E.'54?.0!-, OKJ.%+!ETr@+Ew_C`:ab ( d vHWXG-%+!:'O!:G/5.'5%& 9 Lf,?,J%&)&.0!-,/.)Yon,/.45%&'"( 7 A";: % *!9 F Ej ' c jb?`0@
'
=134("
].'"(. .0,/%&.'E @+En_C`:a ad"
,