Centre for Labour Economics,
London School of Economics
DiscussionPaperNo 349
June 1989
NON-COOPERATIVE
WAGEBARGAINING
by
S. Holden
A DesignatedResearchCentreof ESRC
A bs tra_c t
The pape r
hori zon
argtues
that
automati c
A s tri k e
produc ti on
because
pl ac e.
take
An
the
i ncorporati ng
show n
that
perfect
can
model
c ons equenc e
occ ur
in
thi s
equi l i bri um,
in
c an
perfec t
R ubi ns tei n
al -ternati ng-offers
w age negoti ati ons .
an
the
or
of
other
any
a
c onti nue
probl emati c
is
del ay
as
model
and
equi l i bri um.
of
that
an
w hen
is
a s tri k e
j -s
s tri k es
no
is
l onger
w i th
a l ength
not
negoti ati ons
model
dev el -oped.
a
to
agreement,
al ternati ng-offers
c al l i ng
there
al -s o
appl i ed
ac ti on
reac hi ng
normal -
i nfi ni te-hori z on
c hoi c e
w hen
i ndus tri af
in
i nfi nj -te-
i nformati on
uni que
in
It
is
s ubgame
real
ti rne
2
NON-COOPERATIVE
WAGE BARGATNTNG
S tei nar
H ol den
Introducti on"
ln
ror-onf
s
\/e:rq
cxtensi vel y
thi 'ou11h
n^n-cn^horaJnon-c
ooperati v e i\/6
Lo
the
w age
N ns h
b.trgai ning' -i ,ec ry
ul l ocsi nq
these
perfe.c t
v r.v
ti tc
d ivision
tl l c
si ze
c al c n
tl 'tc
to
to+-a l
be
to
do
rc ' ; c rt u e
the
this
pr oduc ti on
v r age
l e v e l -.
b.ar gai ni n g
wagc
to
'li',,icieci,
" c ati ng
on
ii:
cal:e"
would
c!
t i re . i i r. i .
i ' --
-L e: s
be
the
ciear
the
as
usual
would
could
v rh y
j -n i n g
the
when
a l t e rn a t e l y ,
cake
witl;
one
this
mi g h t
p a rt i e s
l:e
cann:t
re a d i l y
as
s i ro rrl d n ' t
p l -a c e .
tales
wage
b a rg a i n
be
costs
associated
to
re a c h
l rf re i -r
-, -i c ' . ;
th€
cal:,
c c -, r-rt i n L ri :
A
n a t u ra i
c o n t ra c t
p a rt i e s
p a rt i e s
an'j
nodei
l re ri o a l
the
the
O!''t-
vqll(
re a c h e d .
c o i ' rt -ra c t
existing
still
mo t i v a t e
the
fc t-
R ubi ns tei ;t
har-craln
the
p ro b l e m
I , l h rl e
b a rg a
p ro i o n g
but
is
c.,'.'er t,he
to
Th e re
division
i rn p o rt a n t
the
narties
o f f e r-q
t i me ,
n c r; o t i a t j . o n s .
v rh i l e
continue
wtiich
alr
give
over
bas i s
Tn genera.
i 986)
of
i ' .' ,
al ternati ngr-offers
the
w rre re
p a rt i e s
dininish
h o w e v e r,
where
io.l
norr-c ooperat
al .,
i nfi ni te-hori z c n
Th e
a q re e n e n t
io,
a p p J -i e d
c a l r, e .
et
rnnl
i nC i rec --1,
and
on v ari ants
bas ed
,
or
(w here
B i nmore
Case.)
l.'oon
been
a j us ti fi c c i ti on
as
c f.
been
fatert
cake
an
T h e re
is
hav e
a
the
until
us ed
i nformati on
of
of
been
di rec tl y
s ol uti on
poi nts ,
tt,ligq'g111-1t
/fl'ro
\
it
has
hac
has
harcrininry ni ng
bargai
ei ther
bargai ni ng
aFp-l i c .rti ons
rr;lnl
bargai ni ng,
di s agreement
(I9A 2)
r.rado
w
age
over
and
let
the
new
with
an
',,;a1'
the
a g re e me n t ,
J
b ut
th e se
co sts
would
be
consider ably
s m al - l er
than
the
c os ts
to
i n cu rre d
d u ri n q
f- his
situation
would
f eav e
the
uni on
a
in
as
L .a rc;a i n
a tn d
i r-\.-
f,:,:
.rl .- i1e
{ ' ir m
f l te
usually
would
be
on}y
too
happy
to
assum ed
reached.
pr evious
contr act' s
wag es .
T hus
to
i- o
use
a
str ike
or
tv pe
another
of
to
For
utj "l i ty
l ; l sh
An
o r,:l e r
in
put
to
pr essur :e
point
i n p o r.ta n t
on
to
firm
pr esent
the
of
the
c i fer
pa per
a
the
wh ether
on
b ar:q :i n i n c-;
t- o
mo del- .
f n
ca]l-
a
str ike
fact
this
shou l d
can
be
un i on'
i nc or por ated
done
be
by
in
v er y
a
of
p ro p o sa l ,
th e
f or
union
p e ri o d ,
one
Rubinstein- m odel.
the
assum ed
is
unti- I
the
eac h
Aft er
to
pr oposal-
next
not
or
si mil- ar
co n cl r.r-de
h o t;e ve r
m odelthat
used
is
ther e
ar e
in
only
a
t-hat
wh o l e
i nter val.
stri ke
a
<rr hr r - r m o
M or e
with
nor f
onl-
a
( 1988)
Ha l - l - er
.1
oarr
i
l i hri
in
r eal
bar
a r-n tn
of
model
th e
f ir m
has
u, :
fi rm
and
the
union
O if
t he n
li
e
[0 ,1 ],
b o th
the
fir mr s
get
thei r
future
For
s hares .
there
is
a s tri k e
to
hav e
l i near
repres ented
the
peri od
in
agreernent
is
the
di s c ount
H al - l er
the
by
uni on
thi s
is
u. :
t,
Wo if
there
is
to
and u. = W i f
be reac hed,
an
6 is
reac hed.
fac tor.
the
H al l er
tim e
m ay
does
be
fi rm
1- ev e1s ,
c orres pondi -ngty
@
U =
at:r6t.t,,
m ent,i c n
not
w e hav e
does
s us tai ned
as
a
w here
v,
is
no
stri k e
^n
^c rrFement
O if
there
is
a s tri k e
peri od
in
Vt :
t,
1-W o i f
there
rrm
is
the
following.
In
per i od
eac h
of
and
peri o d,
a
value
added
of
one
of
uni t
,i
c J oor l
can
divide
them -
between
'l 'hr '
,ur i on':;
shar e
is
l- W .
If
( ,r l l ::
tl r r .r r ni ( ) n
zer o
.in
that
1r or io,l ,
lrrrl
il
i ::
an
is
agreement
y et
has
to
be
reac hed,
and
v,
:1-l {
reac hed.
are
gi v e
as s umed to
and w i thout
l os s
gi eneral i ty
of
one offer
al ternatel y ,
offers
the
fi rrn
as s umed
is
to
nor m al
an offer
peri od
in
1.
The uni on
c an then
ac c ept
or
rej ec t
it
rej ec ts
thi s
'^'l r j , l r
ff
the
uni on
the
ac c epts ,
bargai ni ng
ends ,
if
the
:;l r ,r r r
hav e
to
dec i de
w hether
to
s tri k e
in
peri od.
thi s
If
the
,r :r t r i fr t',
fj -rm's
p a rti es
be
y et
un-i on w i ll
is
c an
has
offer.
t he
pay offs
and an agreement
gi ve
p r o d u cti o n
thei r
no stri ke
m odel-
the
as s umed
s tr i k e
to
per
se tu p
are
6 t -1 u , ,
t
The parti es
T he
parti es
a
i f
' I he
is
a new agreernent
#-1
u-l
the
of
w age
equi l i br i um
impor tantly,
length
unti l
6
(2)
not
and thi s
gi v en.
is
two
di v i s i on
both
so
s um of
[J =
For
ve ry
A
c ontrac t),
natur af
r ei ec ti on
w hether
deci- de
s i mpJ -i c i ty ,
s
vrhere
c xt-e n si cn
prev ai l i ng
be the
func ti ons ,
( 1)
: l e ci sro n
prev i ous
the
in
uni on' s
the
v ,,ag.,.
hi gher
t,hat
is
w age l ev el
Ini ti al Iy
r i ,r l
i r r c l u:;t
di scounted
a cj --i o n
peri ods .
l ater
rl
1r ,1- l|11
uni on
the
in
I (
.r bl r
be
added
w eal .:
is
p o :: i ti o n
v al ue
j -s W o > O (the
share
Cl e a rl y,
the
affect
str ike.
a
o ffer
is
rej ec ted
the
uni on
gi v es
a ne\d offer
in
the
nex t
,r :',:;r r m c c l not.
peri od,
w hi c h
the
fi rm
ac c epts
or
rej ec ts .
If
the
uni on' s
offer
is
5
6
ac c e p t e d
to
strike
turn
ga m e e n d s,
the
in
n nr Fnn. r -
p e r io d ,
th i- s
give
to
if
an
o ffe r ,
it
is
and
r e je cte d
the
i- n th e
n e xt
Bo th
p a r ti es
e tc.
uni on
peri od
deci de
it
are
is
w hether
the
assumed
fi -rn's
to
have
The
w age
q tr i
pay off
tota]
out c ome
ko
W is
of
the
agreed
(v i ew ed
uni on
upon
peri od
in
peri od
from
s,
after
1)
s -l
if
the
peri ods
of
i <
i h€^r hat ion.
The
s t r u c t ur e
of
th e
g a m e is
illu str ated
in
Fi gure
1 befow ,
O
t ',' h e r e t i r e
gl v e n
a n d th e
fir r n ' s
one peri od
r e sp e ctive
payoffs
are
(3)
us(w) : x
6t w:
:6 '- tu ( w )
6 "" w /( r - 6 )
foral l -s > 0.
t _L-5-t -
p a r e n t h e sis.
in
L -r or t r o
unionrs
For
I
the
fi rm,
w e hav e
c orres pondi ngl y
Period:
1
p r o p o se
fir m :
oo
W,
(4)
\,
union:
v,(w)
:
(1-w )
6t
r
:5s -1
(1-w )/(r-6):
s > 0.
d' -1v (w ) , foratr
+-L-5-a
accept/r ele c l i u
/\
g a m e e n d s,
( w1 1 - w1 )
'
uni on:
stri ke/no
(0, o)
a/
u n io n :
!f r r liL Lr .m .
p r o p o se
\,,
: cvnuosnI Jt L / /
q
/ r o! E
i Jcu L a r f
Dor
nari
nA
pa r e n t h e s i s .
n:rz6f
f
fOf
the
UniOn
is
equi l i bri um
in
ev ery
p r o p o se
and
(o, o)
strike
(w0,1-wo)
w3'
the
f! rrrti(/ rm
_
resner-t
jrro
L r' / e rj ,
lr_.
IN
thi s
proc eedi ng
it
is
games
exogenous.
One j -s the
ori gi nal _
assumed
s tri k e
ev ery
The uni que
perfec t
S haked
S utton,
gi ven
a nd
by
in
the
thi s
game.
of
c ons ti tute
Our
aj -m i s
thi s
a N as h
to
fi nd
c onv enj _ent
to
i nv es ti gate
s tri k e
dec i s i on
is
uni on
R ubi ns tei n-game,
peri od
equi l i bri un
1984),
of
w hi c h
I975)
a
game.
in
di fferent
to
s trategi es
of
s ubgame
w here
(S el ten,
equi l i bri urn
a pai r
equi l i bri um
B efore
strike/no
L/
fir m :
game
perfect
union:
perfec t
bargai ni ng
v
( W2 ,1 - Wz)
(s ubgarne)
A
(w 0,l -w o)
W,
,/
g a m e e n d s,
stri ke
unti t
outc ome
w hen the
fi rm
tak en
w here
the
an agreement
is
w f (c f.
gi v es
R ubi ns tei n,
the
fi rs t
tw o
uni on
as
is
reac hed.
l ^982, or
offer,
is
=
U , (rr" )
u 2 ( w' )
(.)
w" €
=
\', ( ru'")
[0,1]
w here
\' l( wr )
w ere
W' i s
the
give
to
the
The uni que
, , , 'lr c r e r , . ' . ' i s
,,.;cre to
thc
give
p e r fe ct
u n iq u e
Lhe
fir st
ca n
I . ir c r e r
share'-han
.,::-ike
onIl-after
111.i-p
cf
r
'. il
in
.:,""gqYu.
rejecting
the
This
rru
/ lonai- h
th e
nf
its
o r ig in a l
str ike
o ffe r s
ve r y
a n d not
aca
la r g e r
sim ila r
h:rcrinina
deci si on
Ru b in s tei n-game.
:drranf
lrr
to
th an
the
costs
l-he
By
cal l i nc;
fi rmrs,
the
make
of
assumpti on
afl-ar
obtai n
the
WilI
'fhiS
th e
norinrl\
after
to
th a n
) . .:t:1
' J,
a fter
6 i ..'o s
an
The unique
unio n
t-ir'-
is
air r eq
the
advantacr c
p e r fe ct
a s s L r m e d to
f ho
firqt
which,
flr r nr s,
fO
the
nffar
o n ly
t +r a
iq
dS
by
noted
airron
thi s
is
that
the
in
every
thc
costr
:
l{ o +
(r)
nrannqal
Bi nm or e
in
vz(t\j ')
v3( wr )
is
( 1 +6 w o )/e ,+6 )
Wu :
et
a1
hr;
and w hen the
U2 ( liu )
period
other
l ength
of
fol l ow i ng
[0,1]
the
Thi s
s urpl us
is
from
w here
how ev er
the
not
uni on
eac h
peri od
al s o
c omment on the
i -s as s umed
W t,
N ote
reac hed
(1-w o)
,
so
i . e.
in
the
the
uni on
s tr j ,k e
ev ery
an agreement.
as s umed
is
be s ma1l .
c as e w here
to
parti c ul arl y
attrac ti v e,
to
ev er
rec ei v i ng
on
agreement
reac hi ng
v ery
is
( 1-w t ) / (r-6)
to
i denti c al -
i mmedi ate
frorn
that
s trategy .
no agreement
pay off
the
is
an
i bri urn
if
fi rm
prov ed
al s o
is
by any s tri k e
c an ac hi ev e
to
it
f
Thus
w hen the
in
s hal -l s tri k es
s uc h di s rupted
the
are
al l ow e d.
In
games
both
there
bargai ni ng
model - how ev er,
+- l
urr ,,
h^;
is
abov e,
exogenous,
per fec t
w '€
equi l
w here
appendi x ,
(1-w 0) /(L-62),
w hofe
the
An
iq
pay off
reac hi ng
from
the
uni on
peri od.
other
game, v/here the
thi s
o wn proposal -s,
wt,
=
(7)
to
in
the
garfte i s
extracts
ti me
the
bes t
total
thi s
r i
^ .,^
e^1,ar
ua^ .i
U, (I'Jr )
s ol uti on
gi v en
is
th e
payoff
not
o u tco me
a fte r
proof
rej ecti ng
that
rrnianlq
The
cr
UniOn.
e q u ilib r iu m
str ike
uni on
offer.
( w o +6 ) /( L +6 ) ,
w?:
a
\ - *, , Y t J 9 ! 4 v g /
l a r qe r
the
if
uni on
I/ Q+ 6 )
o r ^ ' n p r o p o sa ls,
u n io n ts
is
the
fi rs t
outc ome
equi l i bri um
is
u se
q.1-rateoir-al
a
+ -h c f i - r n ' s .
rJnl
h o we ve r
its
cret
if
(B )
(5)
to
w" :
union
outcome
o ffe r .
T h e l i n . i c l u e so lu tlo n
The
e q u ilib r iu m
perfec t
uni que
. , , -J e l -1 e d ,
e q u i l i b ri a ,
w here
a uni que
it
and
s t ri k e s
In
equi l i bri um.
the
c hoi c e
of
c al l i ng
out
to
an
inf
ma y
aLso
occur
in
be
is
dec i s i on
s tri k e
perfec t
w here
t u rn s
the
inite
tak en
the
as
ri c her
a s tri k e
is
n u mb e r
of
e q u i l i b ri u m.
10
I)r^ n^c
i I
i nn
1
will
rece i v e
peri ods.
aLt
for
l V .e
T h e s t r u ctu r e
Pr o o f :
ot
an )
\i , then
in
the
the
of
su b g a m e .
strategi es
in itia l
th e
is
T h is
done
is
offer
or
dow n to
fo r ce d
in
that
if
acceptance
ot
such
is
one of
( u n io n
a ll
u!!gr
^rc^-
' t sr
Ilnion:
o f fe r
I{0,
Di s r , r p t e d
r e je ct
a ccept
Wo, accept
( fir n
is
a l- l- l{ 1 Wf,
! { u, r e je ct
p e r io d s
alf
uni on
w i fl
c hoos e
uni on
ac c epts
the
nronoses.
In
al l
forced
( i.e .
a cce p t
p e r io d s,
odd-numbered
u n til
W t
W 0, nev er
dow n to
al l -
fact
by
al l
in
in
the
the
wh o
no-strike
enrri
lihrirr-n
in
is
th e
e q u ilib r iu r ,r ,
d e via te s
eq u i J - i b r i u m )
f rr.
p l a ye r
where
u n io n
th e
fr o r n th e
this
a d va n tageous
e q u ilib r iu m
is
nl^vpr
in
to
s tr a t e g y
the
morc
firm
than
u s f i r st
is
can
in ve stig a te
c l ea r ly
r ece ive
Wn. As
fo r
n o - str ike
As
lo n g
1 -
Wn fo r e ve r ,
th e
u n io n ,
if
it
uni on
s tri k e
w hether
the
Iev el
uni on
unl on
nev er
ac c epts
demand W u. Thus ,
al w ay s
as
the
thus
W n.3
the
it
W e then
to
as the
arbi trary
w age
l ater
c annot
hav e
to
after
the
fi rm
a hi gher
ac hi ev e
s how that
is
it
ow n propos al s ,
i ts
in
and
If
by
is
i ts el f,
Wr in
and
uni on
the
c l -earl y
it
s tri k es
will
al l
l ater
mc re
than
peri od
in
peri ods ,
a
pay off
the
totaL
if
t
pay off
z ero
rec ei v e
t,
the
ev en,
in
the
pay off
of
uni on
fai l s
ds
equi l i bri um
will
it
and rec ei v e
f or
the
uni on
be
then
pay off
a total
to
forc ed
s tri k e
of
to
dow n
W s / (1-6).
it
Thus
ow n propos al -s .
after
no-s tri k e
the
w i l -l
be
S i mi l ari l y ,
the
un' i on does
s tri k e
not
in
peri od
stri l .r'
by the
one sw i tch
f i rm,
it
will-
rec ei v e
t,
t
pay off
a total
odd,
of
af ter
a propos a' l
W o + 6l I"/ (1-6)
. Thi s
t.o
is
more
t han
the
pay off
by
c al l i ng
a s tri k e,
6rtl o/(1-6),
henc e
the
nttnish.ed.
th e
o p tim a l.
offer
Thi s
stri ke,
uni on
Let
the
s tri k e,
c urrent,
fac t,
w hat
al -l -
fi rm
(the
di srupted
strategy,
it
agreement.
fi rmts .
an
6\r / (1-6).
it
the
and
not
the
equi l i bri um,
fater
for
does
in
that
W0 in
no
reached.
posi ti on
W f,
l es s
W r i mmedi atel y ,
peri od
opti mal
If
not
offer
the
fo1 Low i ng
uni on),
is
agreement
after
currcnt
stri ke
the
any
is
is,
It
W 0, or
s tri k e
bel ow
credibl e
not
1-w r):
In/ ) w f,
di s rupted
offer
by
it
as
if
if
i nc Ludi ng
s tri k e.
rej ec ts
and
s tr i k c .
al -l - W < w u.
p r o p osal s
a fte r
w S w o'
the
pay off
peri ods ,
to
or
peri od,
that
the
al l
not
l ong
in
than
W n, i n
as w el l
payoff
al l
as
w age
any
Wn):
dow n to
fo r ce d
a l- l- W > Wu a n d a ccept
r e je ct
ev e n - n u m b e r e d
in
W .
e q u ilib r iu m
l{r,
offer
is
W > Wo a n d
aIl-
r eject
strike
offer
get
tw o
fol l ow i ng
the
l es s
then
payof I
mi ni mum
hi s
Thi -s i s
uni on
ni ght
e q u i l i b r ju m
I f i L[r' ' .- '
s tr i k e
p la ye r
d evia tin g
I
un l . o n :
e q u i- Ij- b r iu m
fr o m
parti ti on.2
e q u i ti bri um
e q u i l i b r ia .
fo-5tri}.e
F'irm:
th e
d e via te
folfowing
t yp : e s
of
p l a y er s
the
a p e r fe ct
w* is
W t],
[\i ..,
pay off
z ey o
as
equi ti bri um.
the
uni on
The fi rn's
never
will
ar:cent
not
s tri k e
Wf i mmedi ate' l w .
propos al s
after
othc rw i s e
it
wil,
by
the
fi rrn.
be forc ed
The uni on
dow n to
w i l -l
W^ in
the
stri l :cl ,
f ol l ov,ri ng
to
a n d there
is
no need
st ri kes
in
arry peri od
s ubgame.
offer:
We n ow hav e
t,
t:
peri od,
and that
to
thi s
s how that
offer
will
the
fi rm
w i l -I
be ac c epted.
offer
If
W. in
the
fi rm
the
fi rs t
does
not
L2
11
oIfer
i {,
I i r m's
th e
b e st
c l ea rl y
a n -l
is
to
the
fir m
a
p e ri o d ,
the
n o -stri ke
J i r r u p tcd
n e xt
union
re j ect
the
than
and
the
be]ow
offer i ng
will-
if
an
fai l s
in
w 'i n
l e ve l s
I Irat
Cl ear ly,
]e ss
tva l e
th a n
gives
fi rm
wiff
as
above
above
it
never
can
be
offer )
s uppor ted
is
,
as
the
bel ow
thi s
per fec t
pr ov ed
uni on
the
in
str ikes
\ r ' d e e I e ve l
1 ol I o v r s d i r e c t l y
ori g i n a l
an upper
this
uni o n
strikes
pro o f
that
pro o f
for
in
this
the
th e
w'
in
nr r qqihle.
part
of
o n p la ye r
in
[6w r,
j br i a
e q u ilib r iu m
p e r fe ctn e ss
of
th e
r :annnt
equi ti bri un.
for
u
or - f
Ys
of
(1984)
If
the
payoff
of
an
su b g a m e
R emark
agreement
perfect
d isr u p te d
stri ke
is
is
reachecl .
si mi l ar
equi l i bri um
to
s i tuati on
not
is
thi s
the
a
uni on
Thus ,
is
get
will
pay off
the
peri od
nex t
c al l i ng
6W 6/ (1-6).
the
it
the
i ts
dow n to
forc ed
s tri k e
di s rupted
the
pay off
of
s tri k e
di s rupted
thi s
the
uni on
will
gi v e
will
a
l ev el
do
total
break s
equi l i bri urn
mi ni mum
s ee
by
offer
a total
a
H ow ev er,
bec aus e
w o. To
al s o
an
mos t
at
from
on.
s tri k e,
is
rej ec ts
fi rrn
If
more.
equi l i bri um
the
if
s tri k es ,
uni on
W o.
the
4
A po s s i bLe
the
w hi ch
w here
the
from
by
perfec t
uni que
get
uni on
as the
equi l i bri um
and c annot
l es s
the
as
,
better
is
abl e
then
eqU i l i bri um,
as
be s upported
c oul d
L
proof
The
uni queness
Sh a ked and S utton
a q tr lke
u n ti]
is
p r oof
r r ni on
w t],
perfec t
uni que
the
any thi ng
ac c ept
equi l i bri um
appendi x .
wo is
con s i der
S w /r (1-6)
l - ev el .
p a yo ff.
2's
p e r io d
p e r fe ct
th e
o n e co u l- d d e fin e
e ve r y
fhe
LeLe,
any
m o d e l- cffe r e d
bound
c a se
not
ar e
th a n
fr o m
R u b i n s t ein
In
w0 e
uni on.
to
equi l
neve r
dow n and
cl j q rrrn te d
a lrigher
wo 2 w r,
will
thi s,
per fec t
as
for
for c ed
suppor te d
be
fir st
be
o pti m al
be
never
iJr cannot
the
W' cannot
_2_
Tf
pu t s
it
W n,
L e ve l s
( ' . ..-h e n t.h e
R e na rk
h]n or
onJ -y c hange
3
rf
below
and the
l w o, w r].
to
s hri nk
for
1,
w hi c h
w age l ev el s
of
w oul d
equi l i bri a
R emark
the
QED
e c l u i l i b ri a .
a c ce p t
perfect
range
the
be that
propos i ti on
in
equi l i bri un
the
s ubs ti tuted
the
R e n a rl l
Wa g e
s tri k e
be
c an
equi J -i bri um
s tri k e
The
tr r 'n,
c as e
on
w oul d
so
do
omi tt ed.
thus
di srupted
the
onl y
thi s
aqr eem ent
rn
to
r ec ei v es
bec aus e
ensur e
t}r c
w hi c h
w '.
it
uni on
wr
T hen,
per i od,
nex t
w* bec aus e
foll- ows
pr oposal
fol - l - ow s .
in
payoff
accept
equilibr ium
p e ri o d .
W"
fower
witl
any
stri ke
equilibr ium
accept
equilibr ium
rvi I I
it
str ike
o ption
g j -ve s
first
Lhe
disr upted
to
thi s
agreement
of
ex tens i on
c ommi t
i ts eLf
in
s tri k e
w i -Il -
l as t
is
stri ke
reac hed.
s tops
The
the
the
i tsel f
woul d
and
stri ke
w i thout
w i thi n
the
hav i ng
s ens e
f or
thi s
i rnrnedi atel y )
c apture
model . i s
the
pos s i bl e
reac hed
.
l eas t
ti me
(i f
c os ts
to
>
1
peri ods ,
an agreement
is
if
no
reac hed,
opti on
of
c ommi tti nc -1
uni on
of
s toppi ng
the
an agreement.
a s tri k e,
s tarts
it
s
uni on I s
The uni on
fotJ -ow i ng.
if
that
at
The
the
It
is
tri v i al
to
a
s hc ,' *
L4
13
that
o p t i on
this
pe r f e c t
than
wo u l- d
( th e
equilibria
Wn would
i t s e l f,
"oor*itt"a
be
Wn in
l- o wer
part
th r e a t
n e ver
to
accept
or
b ecause
w hen
the
cr e d ib le ,
p r o fit
wo u L d
fir m
th e
than
wage leve}
fir n r s
lo n g e r
no
th e
r e m o ve
order
sto p
to
from
the
of
lrsp-a-Ei.!j-an-2
any
there
is
a discount
is
the
where
exi s t s
on
reached
Proof:
T h e e q u ilib r iu m
pl a y e r
has
pe r i o d s ,
in
offer
proof
firm
in
any
of
a ll-
l ength
goes
real
to
zero-
as
but
devi ate
in
1 -
if
ex i s t
for
\
6N 11-w .)/(r-6)
to
equi v al -ent
(l -w r)/6n.
s tri c t
l es s
any
c ond.i ti ons
peri od.
l ater
the
in
dev i ates
w o,/( 1-6 ) . Thus
ti me,
in
t imirar
Thus
(9)
the
uni on
bound
upper
the
determi nes
to
not
fi rm
the
pay off
fi rs t
the
to
peri od
by
ac c epti ng
will
not
dev i ate
uni on
pay off
W o, i ts
uni on
bc
will
2 !l n/ (1-6)
6uv l "/(1-6)
if
the
If
A N w -7(1-6).
is
,
or
as
l ong
(10)
no
w - > w ol 6N
W (
accept
W > w* and
W*, r e je ct
e ve n - n u m b e r e d
p e r iods,
al L
W < w *.
W 2 w f,
W < w * and
a ll
S Wo i n
accept
al -I
Wf, a cce pt
al -l - w
no stri ke
in
peri od,
not
stri ke,
and
accept
The same c ondi ti on
N
th e
e q u i J .ib r iu m
giving
in
to
bound
atl
al -l
p la ye r s
th e
d e via te s,
th is
p la ye r
fo ]lo ws.
p a yo ff
to
fir m
th e
fir st
th e
f ir m
th e
p e r io d ,
th e
to ta l
th e
subgame
A
is
5N 11-w ")/(r-6)
d isrupted
p a yo f f
(1-w 0)
stri ke
-
rf
the
goes
N is
now
al s o
=
any
l ater
s how
that
the
w hen the
t he
to
l ength
z ero,
cons tant
N i ncreas es ,
equi l i bri um
+ 6 (r-w u) / G-6)
l\
s tri c t
fes s
Thus
in
ex i s t
c ondi ti ons
peri od.
s tri k e
to
not
uni on
(10)
for
determi nes
the
fi rs t
the
uni on
the
l -ow er
on w .
D enote
the
but
in
d ev i ate
we
odd-
in
descri bed
and s i mi l ar
the
for
appl i es
*
ti me,
p un ish in g
deviates
follows,
an agreement
p e r i o ds.
above
The
o ffe r
th e n
a l- l
r e je ct
a ll
Wu , r e je ct
! ^ J> W * , s t r i k e
rf
w",
o ffe r
N periods,
numbered
w hereupon
fol l ow i ng,
the
> wo a nd
w
a lI
W0 , r e je ct
then
Union:
are
str a te g ie s
w* <
equi J -i bri um
equj -l i bri un
peri od
b a r g a in in g
e a ch
dev i ate
onw .
l,
a perfect
a
h a ve
ca n
is
not
will
d e v ia te d .
offer
Firrn:
str ike s
of
} e n g th
that
(1-w r)/6N
1 -
w 0l 6N ,
I
N p e r io ds,
in
str ike s
u n io n
w* e
a ll-
6 < l- su ch
fa cto r
W*. T h e se
when the
al s o
N > o and
i n te g e r
, w hi c h
fi rm
I
I
I
.,
For
the
I
stri ke).
th e
/ (\-6)
(9)
hi gher
a
Thus
has
uni on
accepti ng
(l -w r)
more
offer
(r -6).
(1-w r)/
of
range
I w 0,/6N , 1 -
w e l et
and
6 is
of
tength
of
eac h
N i nc reas e
adj us ted
] has
aw ay
hav e
c an
peri od
s o that
from
z ero.
the
goes
s o that
QE D
Lo z era.
w hen
} i mi t
the
of
l ength
as A
l ength.
goes
the
reaf
in
l ength
In
A
c orres pondi ngl y ,
a pos i ti v e
a
peri od
bargai ni ng
eac h
bargai ni ng
bounded
(1-w r)/6N
s tri k e
the
to
the
s tri k e
z ero
i nterv al
and
t_ 5
Rem a r k
5
C onc l udi nc l
There
del a y
of
without
this
type
a tso
a n in fin ite
s tr ike
b e fo r e
of
n periods,
f or
in
is
th e
e q u ilib r ia
is
with o u t
proposition
the
number
any
a b o ve
of
is
agreement
th e
The parti es
th e n
sta r ts.
actuaf
equi l i bri um
puni shed
is
devi ati on
An y
As
negoti ate
perfect
the
is
there
The structure
reached.
fo llo win g .
str ike s,
w here
equi l -i bri a
as
abo v e .
6
( l- 9 8 8 )
Rubinstein
per f e c t
to
describes
su b g a m e ,
following
do.
This
mo r e
intuitive.
will
never
mo r e
than
t he
t ha t
bc
optimal
tn
fact
rea c h e d ,
if
e xa m p le ,
forced
th e
fir r n
fir m
fu tu r e ,
th e
W o w h a te ve r
th e
u n io n
may do.
to
th e
profitabte
to
a str ike .
ca ll-
str ike
to
fo r
th e
p r e ve n t
th e
wh e r e
Bo th
u n io n
p a r tie s
th e
p a r tie s
d o w n to
i- ts
m in im u m
h a ve
is
im m e d iatel y.
to
from
o ccu r
outc ome
B i nmore,
1987) ,
sh o ws
p a vo ff
sig n
.
In
thi s
of
by
w eakness,
si gnal
thi s
jt
N ote,
eredi bi l i ty
is
fol l ow i ng
enduri ng
partl '
a
need
ex tens i v el y
for
a s oc i al -
about
will
k i nd
to
of
thc
thi s
(c f.
l -i terature
One mi ght
i s s ue,
prov i de
not
threat
c onv enti on
w hat
ans w er
a more bas i c
s tri k e
a uni on
the
mod.ef,
c onc epts .
refl ec ts
pres ent
the
e.g.
in
new equi l i bri um
w hether
pl ay ers
i nterpretati -on
v /age rev er
a w age
un i on' s
r",echani ca l
is
ri k e
the
one pos s i bJ -e
i ndetermi nac y
determi ne
the
Thus /
the
used.
will
thi s
moder
One pos s i bl e
if
for
to
dev el op
in
is
w hi c h
enouc l h
c redi bl -e.
may ac t
as
c an
be
equi l i bri um
expected.
offer
it
thi s
a
fai ra.
changi ng.
strength
is
uni on
an agreenent
the
Thus,
that
bel i eves
case
to
equi l i bri a
i ndetermi nate.
to
that
i nformati on
of
been purs ued
is
abs trac t
there
l -eft
has
a rgue
an
a mul ti pl i c i ty
is
w hi c h
hi m
opti mal
f i rm
c an be gi ven
sh ow
to
to
reached,
unti ]
str ike
b e lie ve s
str ike s
of
one
in
it
the
if
the
reason
no
makes
a n a g r e ernent
g ive
fir m ' s
Thi s
Sim il- a r ily,
u n til
fir m
has
in
equi l i bri a
that
bel i eves
do
expects
vari ous
r n a k e the
th e
int e r p r e t a t i o n .
is
to
pl aver
a
after
w ou1d
hi msel f
other
th e
in
strike
for
If
but
strategy
p layer
th e
wh a t
For
T h e e q u i l - i b r iu m
strike.
a lso
h e lp s
u n j - o n will
the
wh a t
of
i nterpretati on
p la yerrs
A
i n t e r p r e ta tio n
not
union
o n ly
not
fo llo w i ng
th e
str a te g ie s.
equilibrium
devi a t i o n
o ffe r s
is
probl em,
that
t he
t here
how ever
Rem a r k
c o mme n t s
s tri k e
is
c ons i dered
offer
that
appl i c ati on
of
s tri k e
the
by
bel -ow w * w i l l
threat
how ev er,
of
of
is
thi s
the
threats
to
equi l i bri um
one
be
or
remai n
c redi bl -e
is
is
bargai ni ng
tak en
for
at
to
unfarr,
it
s ol uti on
granted.
W' is
pray ers
both
c ons i dered
i nterpretati on
N as h
outc ome
has
odds
be
anc l
to
w i th
w here
be
a
ttrc
1B
A ppendi x
w e now
!!!l!919!
*
u ' r c r r L vnf L
no- ^
I 'n n nu
n mr lu .lui Jn o cs, T T
.ce
u n ive r sity
r t m anl-
I ' lic h a e l
Hoel
an d t o
Abhinay
for
d iscu ssio n s
Mu th o o
a n d Ar ie l
s ug g e s t i o n s
o n a n e a r ]ie r
f or
E c o n o m ics,
Labour
c hr i s t i a n i a
B an k
f ln a n c i a l
f or n a t i o n
t hc
The
of
I
fo r
paper
o r i gi nal
am gratefuf
r
i dea
for
part
of
and
the
sAF ce n te r
Un ive r sity
of
to
to
paper,
comments
the
and
the
to
A ppl i ed
and
C entre
N A V F,
ESRC
proj ect
rej ect
for
thi s
to
hospi tari ty,
le g a t
to
hel ,pful
grateful
a m a lso
th e ir
is
at
Eco n o m ics,
osl -o.
Ru b in ste in
Kr e d itka sse s
a n d u n e m p lo ym e n t' r
Department
th e
d r a ft.
L SE,
og
s u p p or t.
about
of
hi ghest
(1984)
wish
aftpr
to
thank
harlinrr
-ead
Ar ie l
a fir st
Ru b in ste r n
d r a ft
fo r
rn
the
payoff
of
at
starti ng
paper
the
be
w i tl 'r
assume
wn < 6 wf,
that
th e
a fte r n a tive
is
di scussed
the
absence
of
any
pure
n e g o tia tio n
is
not
to
sa y
th a t
th e
fir m
wo u ld
bel ow .
w hat
costs.
not
prefer
a Low er
fi rm
rn' order
one
offered
ori gi nal
gi v es
w hi c h
to
in
do thi s ,
S hak ed
of
the
the
w e us e
and
R ubi ns tei n-game.
s trateqy
proof
the
N ote
to
14/ (L-6)
.
that
the
total
the
S utton
N ote
uni on
is
rej ects
t hi s
rncst
offer
that
tak en
fi rm
not
s tri k e
than
the
fi rm's
share
the
the
as
I/ (I-6)
the
and
w hi l e
if
at
l -eas t
is
t1
-
offer
it
rej ec ts
. Thus
w 0(1-6)
2,
and the
6t[/ (1-6),
if
l eas t
that
the
any
of f er
s upremum of
(1-6M) /(r-6)
2 is
1
thi s
peri od
offer,
of
the
(rec al ]
that
) .
s trj _k es ,
thi s
D enote
re j ec t
, i mpty i ng
peri od
fi rmrs
it
at
c ertai nl y
pay off
in
thi s
of
peri od
in
in
the
s ubgames
i nfi mum
s tarti ng
get
to
the
3.
a pay off
w i l -l
will
the
rej ec ts
reas t
fi rm
of
peri od
in
fi rm
at
f i rm
s rnal -l er
is
the
get
will-
c an rec ei v e
offer
rf
ri mi t
egui ri bri um,
s ubgame
w o + 6 (1-6M) / (r-6)
gl vi ng
perfec t
the
H enc e
6(1-5M),/(r-6),
thus
N ow c ons i der
l Jow c ons i der
w age.
i denti c aL,
get
uni on.
an upper
s truc tures
c an
the
pay off
the
any
one
w e deri v e
it
.
uni on
3 are
in
9et,
by the
does
f ess
1 and
c an
equal
1-h.'o*6M/ (r-6)
the
4. T h i s
peri od
stri k es ,
gi vi ng
3. I n
the
of
uni on.
an o ffer
uni on
m y p a per.
uni on.
the
s tri k e
part
the
in
t.he uni on
2 -r
in
the
fi rs t
of
share
thrs
to
'w age
R esearch
me to
the
equi l i bri um
exogenous .
for
Osl _o.
r eferri ng
to
uni quenes s
perfec t
the
s i mi l ar
anal y s i s ,
i nfi mum
I
fi nd
pay off
v ery
fo r
thi s
must
1.
to
pos s i bl e
an argume nt
in
try
the
} atter
-
peri od
in
will
rec ei v e
w i thout
uni on
1.
at
s tri k i ng
w i .rl -
pay off,
6(1-6M))/(r-6),
rf
w hi c h
uni on
mos t
it
c ertai nry
S o the
the
rec ei v es
at
ac c ept
any
i nfi mum
equars
of
the
20
M/ ( r - 6 )
.
Setting
M -
(A 1 )
-
wn ( 1 - 6 )
1 -
6(r_-6M),
M / ( t- - 6)
A s abov e,
( A3)
M:
Thus
we o b t a i n
( 1- wo) / ( r + 6)
M:
(A 2 )
t_ - M =
and
( 6 +w n) / (r+6)
perfect
the
uni on
( 6 + w o )/ ( I + 5 )
de r i v e d
in
th e
a p e r fe ct
in
can obtain
is
the
ca se
upper
lim it
e q u ilib r iu m
wh e r e
fo r
u n io n
th e
the
to
w age
uni on
onl v
w as
It
strategy.
a ny stri ke
stri kes
the
fevel
after
ow n
i ts
pro p o s a l s .
W e n o w s h ow th a t
t he
to
can obtain
'l
f
nor ind r v q
Pgr
t he
unj-on
51 4 /( I - 5 )
pa y o f f
at
,
if
fir m
it
e xp e cts
c on sj- d e r
offe r
str ike s,
wiII
th e
if
t1
-
it
in
p e r io d
th e
fir m r s
with o u t
pla n s
w n ( 1 -6 )
not
-
th e
u n io n
a
th u s
to
to
in
fho
fir m
str ike .
i-hp
get
Thus
the
the
starti ng
a ffo r
hv
most
at
offer
an
si mi l ar
share
the
roiar-l-q
will
l -evel - by
very
is
subgames
the
fi r m
a cc ept
ce r ta in ly
W o + 6 ( 1 - 6M ) /( I- 6 ) ,
pa y o f f
;f
w age
supremum of
th e
e q u ilib r iu m
)
-,
thi s
T h e argument
n o w d e n o te s
norinrl rvu
l,E!
u n io n
the
this
re j e c t s
|.
th e
rTrnr
so
We then
most
?
get
in d e ed
a b o ve ,
a n y p e r fe ct
( 1 - 6 M ) / ( I- 6 )
]east
lea s t
r ndu
qlr
and
d e scr ib e d
in
ca n
u n io n
M/ (1-6)
o n e a b o v e.
the
f ir m
'in
I rr
s t r a te g y
strike
th e
gi vi ng
uni on
thi s
get
will
2.
p r o p o sa lthe
str ike ,
th e
str ike .
6 ( 1 - 5 M ) l/( L - 6 ) ,
in
peri od
uni on
will
not
T h e r e fore
the
u n io n
wh ich
equal s
1.
If
will
accept
fi rm
the
uni -on
at
recei ve
any
can
l "ow er
get
at
is
the
equi fi bri um,
c an
ow n propos al s ,
Thus
y i el ds
(1-w o)/(r+ 5)
(6+w 0)/(r+ 6)
any
thi s
i ndeed
but
not
hi ghes t
w hen the
get
thi s
after
( 6 +w o ) /( r +6 )
1-M:
and
w age
fi rm
w age
the
]ev ef
gi v es
l -ev el -
fi rrnrs .
if
the
the
it
eE D
uni on
fi rs t
s tri k es
c an
ger
offer,
after
l -n
and
2I
CENTRE FOR I.ABOUR ECONOMICS
Re f e r e n c e s
Blnmore,
(1987).
K.G.
P h i f o s o p h y,
3,
K. G. ,
Binmore,
of
Haj-ler,
H.
paper,
BB-09-02,
A.
Rubinstein,
theory.
Selten,
R.
A.
Shaked,
sta te
(1988).
(1985).
perfect
and
b a r g a in in g
as
p o in ts
4,
e q u ilib r iu m
a
The
R and
game.
strategi c
V i rgi ni a
o f Eco n omi cs,
The
in
e q u ilib r iu r n
on
in
th e
e xte n sive
th e
perfectness
g a mes.
Internati onal
(1984).
in
In vo l untary
a b a r g a in in g
model .
+L^
^f
pol ytechni c
model .
of
concept
game
E conometri ca,
1
^l
ffom Centfe
fof
S t re e t ,
London,
L a b o u r E c o n o mi c s ,
WC2A 2AE.)
N o.303
w . B U ITE R
Can Public
N o.304
C. PISSARIDES
U n e mp l o y me n t a n d Ma c ro e c o n o mi c s :
I n a u g u ra l
L e c t u re
N o.305
S. I L MA K U N N A S
AND S . P U D N E Y
A Mo d e l o f Fe ma l e L a b o u r S u p p l y
P re s e n c e o f H o u rs R e s t ri c t i o n s
in
N o.306
W. B U I TE R
A Viable
Mo n e t a ry
Fl e x i b l e
N o.307
D . B I -A N C H FL O W E R
AND A. OSWALD
Th e D e re rmi n a ri o n
N o.308
R. IAYARD AND
S. N I C K E L L
I s U n e mp l o y me n c L o w e r
O v e r E mp l o y me n c ?
N o.3O 9
R.
R,
D o e s L o n g -Te rm U n e mp l o y me n t R e d u c e a P e rs o n ' s
C h a n c e o f a J o b ? : A Ti me -s e ri e s
Te s t
No . 310
R. JACKI,IAN,
R. I^AYARD AND
S. S A V O U R I
J A C K MA N A N D
IAYARD
I ^ I a g e s a n d P ri v a t e
Spending
Cuts
f n f o rma t i o n
be
I n f l a t i o n a ry ?
as
a
G o I d S t a n d a rd R e q u i re s
a n d Fi s e a l
Policy
of
W h i t e -C o l l a r
if
Unions
An
rh e
pay
B a rg a i n
IDETAYEDI
N o.311
S. W A D H I i A N I A N D
M. WALL
Th e E f f e c t s
o f P ro f i r-S h a ri n g
o n E mp l o y me n r,
W a g e s , S t o c k R e t u rn s
a n d P ro d u c t i v i t y :
E v i d e n c e f rc m U K Mi c ro -D a t a
N o.3l 2
W. B U I TE R
S o me Th o u g h c s
in Stabilisation
in Developing
N o.313
s . w A D H w A -N rA N D
M. I{ALL
A D i re c t
Te s t o f t h e
U s i n g U K Mi c ro -D a t a
N o.314
D . ME TC A L F
l^Iater Notes
N o . 315
l ^J . B U I TE R
D e b t N e u t ra l i t y ,
R e d i s t ri b u t i o n
and
C o n s u me r H e t e ro g e n e i t y :
A S u rv e y a n d S o me
Extensions.
Also,
D e b t N e u t ra l i t y ,
P ro f e s s o r
V i c k re y
a n d H e n ry G e o rg e ' s
Ta x "
"Single
N o.3l 6
S. E S TR I N A N D
D. JONES
C a n E mp l o y e e
for
Journal
unempl oyment
^ --^ i
S t ri k e s ,
52,
t _ 35 1 - l _ 3 6 4 .
I
^ .-^
S. Mc C O N N E L L
25-55.
J.
v ! u rrc s c p a p e f s a f e a w a i l a b l e
Sc h o o l o f E c o n o mi c s ,
Houghton
N o.302
88/I8I.
,
of
^^
I,Jorki ng
a bargai ni ng
j -nterpretati on
a^^:
\v v pr s s
London
Journaf
9 1 - IO9 .
Co m m e n ts
/
N ash
u n ive r sity.
Re - e xa m in a tio n
Su tto n ,
( 1986) .
A.
m odel l i ng.
e co n o m ic
Pe r fe ct
50,
G a m e Th e o r v,
A.
Wo linsky,
ST ICERD Discu ssi
equi-librium
of
,
and
De p a r tm e n t
(1982).
E c o n o m e t r i ca
in
wa g e
and
and
176-188.
17,
(1988).
institute
Rublnstein,
A.
so lu tio n
E c o n o mics,
E conomi cs
I7 9 - 2 1 - 4 .
Ru b j- n ste in ,
bargaining
pl ayers.
r a tio n a l
M o d e L lin g
o n t h e R o I e o f Fi s c a l
Policy
a n d S t ru c t u ra l
A d j u s t me n t
C o u n t ri e s
Efficiency
w a g e Mo d e l
D ry U p
O w n e d Fi rms
S u rv i v e ?
On- The- Job
N o .3 1 8
S.
J.
E S T RIN AND
S V E JNAR
Estimates
of Static
W age Deter m ination
N o .3 1 9
D.
A.
M.
B IA N CHFLOW ER,
OSWALD AND
GARRETT
Insider
N o .3 2 0
D . ME T C ALF
Tr ade Unions and Ec onom i c
Evidence
Br itish
N o .3 2 1
R . I-A Y A RD AND
C. BEAN
l^lhy Does Unemploym ent
N o .3 2 2
A.
J.
Styli- sed
N o.3 2 4
N o.3 2 5
N o.3 2 6
N E WE LL AND
S Y MONS
in
Power
Facts
D . B U .NCHFLOWER
AND A. OSI,IALD
The Econom ic
Unions
D. R OB E RTSONAND
J. S Y MONS
The Occupacional
Childr en
A.
S.
B E N-NER AND
E S T RIN
Unions
Ver sus
N o.336
W. B E N TL E Y MA C L E O D L a b o u r Tu rn o v e r
and.the
AND J . MA L C O MS O N
U n e mp l o y me n t :
Efficiency
Unemployment
N o.337
W. B E N TL E Y MA C L E O D W a g e P re mi u ms a n d P ro f i t
AND J . ' MA L C O MS O N
Efficiency
\ ^ I a g e Mo d e l s
N o.3i 8
G. B R L TN E L L O
W a g e D e t e rmi n a t i o n
i n a S i mp l e
Mo d e l w i t h a N o n z e ro P ro b a b i l i t y
P ro mo t i o n
N o.339
D . B L A N C H FL O W E R
N, MILLWARD AND
A. O S W A L D
Unionization
N o.340
D . B I -A N C H FL O W E R
AND A. OSWALD
Th e W a e e C u rv e
No . 341
R. IAYARD
AND R . J A C K MA N
Th e R e a I
P o l -i c i e s
N o.342
A.
Th re e S q u e e z e s :
D e p re s s i o n s
N o.343
R. I"AYARD AND
S. N I C K E L L
Th e Th a t c h e r
N o.344
D.
Fe a r,
l J o.345
D . B I A N C H FL O W E R
AND A. OSWALD
L l a g e s a n d H o u s e P ri c e s :
Evidence
lTo . 346
R.
ll,YARD
Layoffs
by
Employment
N o.347
J.
A.
S I ' } , I O N SA N D
NEWELL
Th e P a s s i n g
U nem pl oy m ent
N o.348
S. H O L D E N
W a g e D ri f t
Norway
F our
N o.349
S. H O L D E N
N o n -C o o p e ra t i v e
Wage D eter m i nati on
Bust
The Canadian
R.
of
Effects
Per for m anc e:
of
Ch oi c e
of
R.
Review
N o.3 2 9
M. MUL L INS AND
S. WADHWANI
The Effect
Investment:
of the Stoc k M ar k et on
A Comparative
Study
N o.3 3 0
G. B RU NELLO
Hyster esis
Pr oblem'
and
N o.3 3 1
C . P IS S A RIDES AND
R. MOGLIADAM
Relative
Countries
N o .3 3 2
C . B E A N AND
A. GAVOSTO
and
Capacity
Shor tages
Outsider s
Kingdom
Unemployment
in the United
N o .3 3 3
J.
and Sear c h
Unemploym ent Benefit s
in the UK Labour Market
N o .3 3 4
S . N ICK ELL AND
S. WADHWANI
WA D SWORTH
Insider
NEWELL
of an Agi ng
of Ins i der -
B I -A N C H FL O ' v J E R
W or k 1987/88
J apanes e
Wage Flexib i l i ty
For ces
a n d E mp l o y me n t
H i e ra rc h i a l
of
Behaviour
Effeccs
of
Ta x -B a s e d
I n c o me s
Th e D e ma n d f o r
Labour
D u ri n g
in
Mi ra c l e ?
F i r r ns
No . 328
' The
in
Ma x i mi z a t i o n
Br i ti s h
Unem ploym ent Conseq uenc es
Population:
An Appl i c ati on
Outsider
Theor y
Year ' s
N a t u ra l
Rate of
\ ^ l a g e v s Fri c t i o n a l
T r ade
Br i tai n's
C. P IS S ARIDES
the
C o u n t ri e s
P e rs p e c t i v e
'82
U ni oni z ed
and Pr oducciv i ty :
Union M anaged F i r m s
of
W a g e Fo rma t i o n
i n t h e N o rd i c
V i e w e d f ro m a n I n t e rn a t i o n a l
D em and C ur v e
N o.3 2 7
I-AYARD
T he
Per s i s t?
Labour
J A C K MA N
Ev i denc e
and D y nam i c M odel s of
Firms
i n Labor - M anaged
and the
M. K E IL AND
J. S Y MONS
N o.335
Som e Em pi r i c al
C , P IS S A RIDES
AND J. I./ADSI^IORTH
N o .3 2 3
I'
Sear ch:
N o .3 1 7
Effor t
and l J age D eter m i nati on
U n e mp l o y me n t
S e n i o ri t y
of
the
a n d P a y Fl e x i b i l i t y
C ro s s -s e c t i o n
a n d E q u i l i b ri u m
Golden
a n d B a rg a i n i n g :
Age
Evidence
l , l a g e B a rg a i n i n g
f ro m