m qm !m "m

T

q!m ! !m

"m

!", "", !# " (0, 1) i

ui(#" + (1# #)"") > #ui(") + (1# #)ui("")

"!m

!

! !!

!"

!"

!!

Xm

Ym

!m

! k

k Y km m

m!

k !kY k

m

! = .12

Ym

!Ym ="

k

! kY km.

Ym !Ym

! !m Ym

!

!

! !m

!m "(i, !m)

i !m

!!m

!!m

!!mS

!!S "m(!!S)

"(i, !!S)

m "m(!!S)

# $

s2S =

!m"S(Nm ! 1)s2m +

!m"S

!m!"S

NmNm! (!m#!m! )2

2NS

NS ! 1

#(·, ·)2|M | %M sM 2|M | #

%M sM

# $

s2S S

%S %S!

(%S ! %S!)2

#

s2S " (1 + &S), &S # N(0,2

NS ! 1)

" &S

!m!m!NmNm!

NS(!m ! !m!)2 = !m!m!

NmNm!NS

((!m ! !)! (!m! ! !))2 = !m!m!NmNm!

NS((!m ! !)2 +

(!m! ! !)2)

!S !S!NS"S!

!NS

!NS!

NS"S! !

"

S (") S #|S # "

S (") S #|S # " S # "

S (") " S (")

S

S

S # " S S # "

S #

S \S #

!S $ N(% 1NS

% 13N2

S, 2NS!1 )!

NS!12 !S $ N(%

"NS!1"2NS

%"NS!1

3"2N2

S

, 1) NS

! !!("(#M , sM)|X, $)

!S " " S (!) vmm($) + "m(#M , sM) > vmS!($) + "S!(#M , sM)

vm!m!($) + "m!(#M , sM) > vm!S!($) + "S!(#M , sM)

S " = {m,m"}

!S " " S (!) #m " S " vmS($) + "S(#M , sM) > vmS!($) + "S!(#M , sM)

S m ! S " $ S

!S " " S (!)m#S

(vmS($)% vmS!($)) > "S!(#M , sM)% "S(#M , sM)

S ! S

! "

# s

h!!(!|$, X) = h(#M , sM |X)

+!

S

h(#M , sM |X) S

! $ X

$ h!!

(#m % #m!)2 m

m" s2m m

h

h!!

FQ(!)

FQ(!) F 79Q (!)

FQ

S

µ!Q

EQg2(Q79, !0|X) = µ79

Q ! µ!Q(!

0|X)

" µ79Q ! µQ

µ!Q

S = {m,m"} umS > umm um!S > um!m!

m m" S

Sa

Sa "M

sM

Q! =Q#M

Q #S $ Sa, S %Q &= '

Q! Sa

Q!

Q! F !Q(!) Q! FQ

F !Q Sa

Q!

Q!

J J J

g1 (!) g1 J

g1 (!) =1

J

!

j"J

g1("0j , !|X)

g2 g3

!0j j g2

g2

g2 (") =1

J

!

j!J

g2(Q79j , "|X)

Q79j

j

g1

g2 g3

"

g3 (") =1

J

!

j!J

g3(Q99j , "|X)

Q99j

j

# s

g3g1 !0 g4

(")

"

" =!

(").

{!| (!) < (!) + 0.95(!)}

0.95(!)

! = ! !

g1

! = 0

J Aj Bj

Sj = {Aj, Bj}"j

uAjAj = uBjBj = !

uAjSj = uBjSj = 2! + "j

"j ! N(0, 1)

! #0

j {Aj} {Bj} {Aj, Bj}

R(!, "|#) : !j " J, !j # $# {Aj}, {Bj} " "

!j % $# {Aj, Bj} " "

h(!) =!

j!J !2j E(h) = |J |

!"(#) =!

h(!) R(!, "0|#).

!"(#)

h "0 h

h"(#) =!

h(!) R(!, "0|#).

!0 "0

#0 #

h"(#0) # h(!0)

!0 "0 R(!0, "0|#0)

E(h(!))$ E(h"(#0)) % 0,

E(h"(#0)) h"

! !

!(#0)

h"(#)

!(#0) (0, #)2 + (1$ !(#0)) (0, #)2

{# | 1$ !(#0) (0, #)2 + (1$ !(#0)) (0, #)2 % 0}

[ !1!!(!0)

, 1!1!!(!0)

]

! = 0

! = 0

K {m1,m2}{m1,m2,m3} {m1,m2, ...,mK}

umkS =S

K+!K!j , S "= {mk}

umkmk = k # K # 1

2

S S j! = 0

K

umkS = (1# ")(S

K+K1/3!j) + "(k # K + 10

2+ !2j ), S "= {mk}

umkmk = k # K # 1

2

" = 1 !

" "0 = 0

K " = 1"0 " = 1

!!

!

E[W (T )] = (" = {S}|T )((wm + wm!)(vmS(TS) + E[!S|" = {S}, T ])! bTS)

+(1! (" = {S}|T ))(wm(vmm(Tm) + E[!m|" = {m,m!}, T ])

+wm!(vm!m!(Tm!) + E[!m! |" = {m,m!}, T ])! b(Tm + Tm!))

Tm

vmm(Tm)+ !m = vmS(TS)+ !S

#E[W (T )]

#Tm=# ({S}|T )

#Tm(b(Tm + Tm! ! TS) + wm!e!)

+ (1! ({S}|T ))(wm#vmm(Tm)

#Tm! b)

#E[W (T )]

#TS=# ({S}|T )

#TS(b(Tm + Tm! ! TS) + $wm!e! + (1! $)wme)

+ ({S}|T )((wm + wm!)#vmS(TS)

#TS! b)

m

m!

T

T

Tm + Tm! > TS

TS Tm

({S}|T )

vmS ! vmm vm!S ! vm!m!! ({S}|T )

!vmS= !! ({S}|T )

!vmm

m!

! ({S}|T )!TS

/!v.S!TS

= !! ({S}|T )!Tm

/!vmm

!Tm! ! ({S}|T )

!Tm!/!vm!m!

!Tm!

T

({S}|T )

({S}|T ") =(Tm ! T "

m) + (Tm! ! T "m!)

(Tm ! T "m) + (Tm! ! T "

m!) + (T "S ! TS )

!vmm!Tm

= "0+"1

Tm#Ym+"3c(Xm)

1!vmm!Tm

|Tm

! 1!vmm!Tm

=1

"0 + "1(Tm ! T "

m)

!vmm!Tm|

Tm

= bw

(wm!vmm(Tm)

!Tm! b) = b

!vmm(Tm)

!Tm

1

"0 + "1(Tm ! T "

m)

! ({S}|T )!Tm

! ({S}|T )!Tm!

Optimal merger incentive (¥ per capita)

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!

c0

c0

I

T

!!S ! !m !S ! !m!

e

!