A behavioral analysis of learning curve strategy

HD28

.M41A

A

Behavioral

Analysis

of

Learning

Curve

Strategy

John

D.

Sterman,

Rebecca

Henderson,

Eric

D.

Beinhocker

and

Lee

I.

Newman

A

BEHAVIORAL

ANALYSIS

OF

LEARNING

CURVE

STRATEGY

John

D.

Sterman*,

Rebecca

Henderson*,

Eric D.

Beinhocke^^

and Lee

I

Newman^

Abstract

Priorresearch

on

firm strategyin thepresence

of

learning curves suggeststhatiflearningis

highly appropriable, early entrants

can

achievesustained competitiveadvantage

by

rapidly building

capacity

and

by

pricingaggressively to

preempt

competition.

However

these studies all

presume

(1) rational actors

and

(2) equilibrium,

implying

marketsclearatall pointsintime.

We

consider

therobustnessoftheaggressive strategy in thepresence of(1)

boundedly

rational agents

and

(2) a

capacity acquisition lag.

Agents

are

endowed

with highlocal rationalitybutimperfect

understanding ofthe feedback structure ofthe market; they use intendedlyrational heuristics to

forecast

demand,

acquire capacity,

and

set prices.

These

heuristics are

grounded

inempirical study

and

experimental test.

Using

asimulationofthe

duopoly

case

we

show

theaggressive learning

curve strategy

becomes

suboptimal

when

the

market

is

dynamically

complex.

When

capacity

cannot be adjustedinstantaneously, forecasting errors leadingtoexcess capacity

can

overwhelm

the costadvantage conferred

by

the learning curve.

We

explorethesensitivity ofthe results tothe

feedback

complexity

ofthe

market

and

therationality oftheagents' decision

making

procedures.

The

results highlight the

danger

ofextrapolating

from

equilibrium

models

ofrationalactors tothe

formulation ofstrategic prescriptions

and

demonstrate

how

disequilibrium behavior

and

bounded

rationalitycan be incorporatedintostrategic analysisto

form

a 'behavioral

game

theory'

amenable

to rigorous analysis.

'

Sloan

School

of

Management,

Massachusetts

Institute of

Technology

^

_McKinsey

&

_Company

Pleasedirect

correspondence

to

John

Sterman

atthe

MIT

Sloan

School

of

Management, 50

Memorial

Drive,

E53-351, Cambridge,

MA

02142,

orto

<jsterman@mit.edu>.

1.

Introduction

Learning

curves

have

been

identified in a

wide

variety ofindustries(Dutton

and

Thomas,

1984),

and

an extensivetheoreticalliterature has exploredtheirstrategic implications.

A

learning

curve createsa positivefeedback loop

by

which

a small initial

market

shareadvantage leadsto

greaterproduction experience,

lower

unit costs,

lower

prices

and

still greater

market

share

advantage. In general, the literaturesuggeststhat inthepresence oflearningcurves

-

and

when

learning is privatelyappropriable

- fmns

should pursue an aggressive strategy in

which

they seek

to

preempt

their rivals,

expand

output

and

reduceprice

below

the short-runprofit

maximizing

level

(Spence, 1981;

Fudenberg and

Tirole, 1983, 1986; Tirole, 1990). Intuitively,

such

aggressive

strategiesare superior

because

they increase bothindustry

demand

and

theaggressive firm'sshare

ofthat

demand,

boosting cumulative

volume,

reducing futurecosts

and

building sustained

competitive

advantage

until the firm

dominates

themarket.

The

desirability of aggressivestrategies

in industrieswithlearningcurves hasdiffused

widely

inbusiness education, the popular business

literature,

management

texts,

and

publicpolicy debates (Rothschild 1990,

Hax

and

Majluf

1984;

Oster, 1990; Porter, 1980;

Krugman,

1990).

and

learningcurve strategies

appear

to

have

ledto

sustained

advantage

inindustries

such

as synthetic fibers, bulk chemicals

and

disposable diapers

(Shaw

and

Shaw

1984;

Lieberman

1984,

Ghemawat

1984,

Poner

1984).

However

in

many

industries, includingtelevisions,

VCRs,

semiconductors, toys

and

games,

lighting

equipment,

snowmobiles,

hand

calculators,tennis

equipment,

bicycles,chain

saws,

running

shoes

and

vacuum

cleaners,aggressive pricing

and

capacity

expansion

have

ledto

substantialovercapacity

and

price

wars

that

have

destroyedindustry profitability (Beinhocker,

1991; Salter, 1969; Porter, 1980; Saporito, 1992;

The

Economist,

1991;

Business

Week,

1992).

Existing

models

thatconsiderthecompetitive imphcations ofthe learning curveutilizethe

traditional

assumption

thatmarkets clearatallpointsintime.

Market

clearing inturn implies thata

firm's production capacity

and

other resources

can be

adjusted instantaneouslytoequilibrium

levels, or, ifthere are capacity adjustmentlags, thatfirms

have

perfect foresight

such

thatthey

can

asit is needed. Neither

assumption

is valid: it takestime tobuild

new

factories,

expand

existing

ones,

and

decommission

obsolete

ones

(Mayer

1960,

Jorgenson

and Stephenson

1967),

and

forecastingovertypical planning horizons

remains

difficult

and

error-prone

(Armstrong

1985,

Makridakis

etal. 1982,

Makridakis

etal. 1993).

The

presumption

in theliterature is thatcapacity

adjustment

and

forecasterrorcorrection are fastrelative tothe

dynamics

ofthe learning curve so

thatthe

assumption

ofperfect

market

clearingis areasonable approximation.

Inthis paper

we

show

thatrelaxing the

assumptions

of instantaneous

market

clearing

and

perfect foresight leads, ina variety ofplausible circumstances,tocompetitive

dynamics

significantly different

from

those predicted

by

much

ofthe existing literature.

We

begin witha

review

oftheliterature

on

strategy inthepresence oflearning curves.

We

then

develop

a

model

in

which

the assumptions of

market

clearing

and

rationalityarereplaced

by

adisequihbrium,

behavioral

framework

in

which

fums

face lags in adjustingcapacity

and

use

boundedly

rational

decisionheuristics to setprices

and

forecast

demand.

We

usethe

model

toexploretheimpact of an

aggressive learning-curve strategyin a varietyof environments.

When

the

dynamics

ofthe

market

are sufficiently slow,delays ininformationacquisition,

decision

making,

and system

response are sufficiently short,

and

thecognitive

demands

on

the

firms aresufficiently low,behavioral theory yieldspredictions observationally indistinguishable

from

those of equilibrium models.

However

in

more dynamic

environments,in

which

boundedly

rational forecastingtechniques

become

less accurate, the aggressivelearningcurve strategies

prescribedinthe

game

theory literature

become

inferior, asaggressive

expansion

leadstoexcess

capacity.

We

closewithimplications forthestudyofstrategic competitioningeneral,arguingthat

the neoclassical assumptions of equilibrium

and

rationality

may

in

many

realisticcircumstances

prove

to

be

a

dangerous

guidetoaction

and

a

weak

basisforempirical research.

2.

Models

of

Learning

Curve

Strategy

Learning

curvesare a familiar

phenomena.

Numerous

empiricalstudies

have

documented

theirexistence in a

wide

variety ofindustries, as

Hax

and Majluf

(1984, 112) note, "ranging

from

Spence

(1979)

examines

theeffectof competitive

asymmetries on

investmentdecisionsin

growth

markets

where

there are learningeffects.

He

notes thatlearningcurves allow forcreation of

asymmetric advantage and

thus create

an

incentive to

preempt

rivals.

Spence

(1981) further

quantifies optimal production policy

under

alearning curve, finding thatiffinns

can

perfectly

appropriate all thebenefitsoflearning,

and

ifthey can

be

sure ofafirst

mover

position, then they

should

expand

output

beyond

the short-run profit

maximizing

level inordertocapture

learning-induced

costadvantage.

Fudenberg and

Tirole (1986)

and

Tirole (1990)present a

dynamic

analysisof a

duopoly

with alearning curve.

Under

quantity competition they findthatan

aggressive strategy

always

dominates.

Under

pricecompetitionthe aggressive strategysucceeds in

deterringrivalentry

and

in causingrival exit,but

when

two

existingplayers prefer

accommodation

thereis

no

clearly

dominant

strategy apriori.

Other

studies

have

examined

the sensitivity ofthese results todiffering

demand

conditions

and

appropriability assumptions.

Majd

and Pindyck

(1989)

show

that uncertaintyin future prices

reducesthe optimal expansion of output

beyond

the staticequilibriumlevel.

Ghemawat

and

Spence

(1985)

show

that

when

theeffects oflearningspill

over

to competitorsthe incentives to

expand

output are also reduced. Similarconclusions are

found

in theliterature

on

theeffects of

learning

on

international trade

(Krugman,

1987).

Kalish (1983) addresses the interaction

between

learning

and

productdiffusion

dynamics

(word

of

mouth,

saturation).

Word

of

mouth

creates a

shadow

benefitofcurrent salesthat

reinforces the incentive tocut price

and

expand

production as currentoutputbuilds theinstalled

base of

customers

who

in turn

convey

information

on

the benefitsoftheproducttothose

who

have

not yet purchased, accelerating product adopfion.

In

sum,

the literature suggeststhat iflearning is appropriable, ifprice is not highly

uncertain,

and

ifrivals

can be

relied

on

to

behave

rationally, then firms should pursue an

aggressivestrategy of preemption, higher output

and lower

prices. This

recommendation

has

diffused

widely

inbusiness education, the popular businessliterature,

and

public policy debates

the firm's capacity is

always

equalto

demand, implying

either thatthere are

no

capacity adjustment

delaysorthatfirms

have

perfect foresight so thattheycan forecast

demand

sufficiently far in

advance

toensurethatthey

always have

exactly the correct capacity.

3.

A

Boundedly

Rational,

Disequilibrium

Model

To

explore therobustness ofthelearningcurve literature tothe assumptions ofperfect

foresight

and

instantaneous

market

clearing,

we

developed

adisequilibrium, behavioral

model

of

competitive

dynamics

inthepresence oflearning.

Following

Kalish(1983),

we

assume

that the

market goes

througha life-cycleof growth, peak,

and

saturation. In contrast tothe literature,

we

assume

capacity adjusts with alag,

and

that firms

have

onlya limited ability toforecast future

sales.

These

assumptions areconsistent with a longtraditionof experimental

and

empirical

evidence

(Brehmer

1992,

Collopy

and

Armstrong

1992, Diehl

and Sterman

1995,

Kampmann

1992,

Mahajan

et al. 1990, Paich

and

Sterman

1993, Parker 1994.

Rao

1985,

Sterman

1989a,

1989b, 1994). In

models assuming

instantaneous

market

clearing

and

perfect foresight,the

market

clearing price can be derivedasanecessary property ofequilibrium, giventhe capacity decision.

However

in disequilibrium settings,bothprice

and

capacity targets

must be

determined.

Here

we

draw

on

the literature cited

above and

thewell-establishedtraditionof

boundedly

rationalmodels,

and

assume

that firms setprices with intendedlyrational decisionheuristics(Cyert

and

March,

1963/1992;

Forrester 1961;

Simon

1976, 1979, 1982;

Morecroft

1985).

The model

is formulatedincontinuous time as a setof nonlineardifferentialequations.

Since

no

analytic solution tothe

model

is

known,

we

usesimulation toexplore its

dynamics'

While

the

model

portrays

an

industry with an arbitrary

number

of firms i

=

{ 1, ..., n},

we

restrict

ourselves to n

=

2 inthesimulationexperiments below.

We

begin

by

laying out the equations

describingthe

dynamics

of

demand.

These

are

based

on

thestandard

Bass

diffusion

model

(Bass,

1969;

Mahajan

etal. 1990).

We

then describe the physical

and

institutionalstructure ofthefirm,

including orderfulfillment,

revenue

and

cost,thecapacity acquisition lag,

and

the learning curve.

Finally

we

discuss firmstrategy. Thissection is theheartofthe

model

and

contains the

key

Industry

Demand

The

total industryorderrate, Q", is the

sum

of

theinitial

and

replacement purchase rates,

Q'

and

(^

(time subscripts are omittedforclarity):

qo

₌

_Q'

+

Q«. (1)

Initialorders are given

by

theproduct oftherateat

which

households

choose

to adopttheproduct

and

thus enter the

market and

theaverage

number

ofunits ordered per household, |J.

The

adoption

rate is therate

of

change

ofthe

number

ofadopters,

M,

thus:

Q'

=

|i(dM/dt). (2)

Households

aredivided intoadopters oftheproduct,

M,

and

potential adopters, N.

Following

the

standard

Bass

diffusion

model

adoption arisesthrough an

autonomous

component

and

through

word

of

mouth

encounters with those

who

already

own

theproduct:

dM/dt =

N(a

+

pM/POP)

(3)

where

a

is a constant fractional propensity for potential adopterstoadopt, (3 is thefractional rateat

which

potential adopters

choose

toadopt given thatthey

have

an encounter with anadopter,

and

theratio

N4/POP

isthe probability thatagiven

nonadopter

encountersan adopter

(POP

isthetotal

number

of households).

The

number

ofpotential adopters remaining,

N,

is thedifference

between

the

number

of

people

who

will ever adopttheproduct,

M*,

and

the

number

that

have adopted

theproduct todate:

N

=

MAX(0, M*

-

M)

₍₄₎

where

the

MAX

functionensures that

N

remains

nonnegative

even

inthecase

where

M*

drops

below

M

(as could

happen

ifthe price

suddenly

roseafter

M

=

M*).

The number

of people

who

willeventually

choose

toadopt,

M',

istheequilibrium industry

demand

and

isa function ofthe price oftheproduct.

For

simplicity

we

assume

alinear

demand

curve

between

the constraints

<

M*

< POP:

M*

=

MAX(0,

MIN(POP, POP'

+

a(P"''" - P'))) (5)

where

a

is theslope

of

the

demand

curve, P"^'" is thelowestpricecurrently available in themarket,

The

replacement orderrate, Q"^, isthediscardrateofoldunits, D.

summed

overall firmsin

the industry.

For

simplicity

we

assume

exponential discards

from

the installed baseof

each

finn:

Q'

=

li Di. (6)

Di

=

5li (7)

where

I,isthe installedbase of firmi'sproduct

and 5

isthe fractionaldiscardrate.

The

installed

baseis increased

by

shipments, Qj,

and

decreased

by

discards:

li

=

1(Q. - D,)dt

+

lio. (8)

Each

firm receives orders

O,

equal toa shareofthe industry orderrate.

The

firm'sorder

share. S^j, is

determined

by

alogit

model

in

which

product attractiveness.

A, depends on

both

price

and

availability. Availabilityis

measured by

thefirm'saveragedelivery delay,given (by

Little's

Law)

by

theratioof backlog, B,to shipments, Q):

Oi

=

S°i

Q°

(9)

SOi

=

Ai/IjAj

(10)

A

i

=

[EXP(epPi/P*)][EXP(ea(Bi/Q,)/T)). (11)

Both

price

and

deliverydelay are normalized

by

reference values(P*

and

x', respectively)in the

determination ofattractiveness.

The

parametersEp

and

£a are the sensitivitiesofattractiveness to

price

and

availability, respectively.

Note

that

because

thisis a disequilibrium model, orders

and

shipments

need

notbe equal.

Market

share, definedas

each

firm'sshare ofindustry shipments.

Si

=

Q/Z,Qj, will ingeneral equalthe firm's ordershare only in equilibrium.

The

Firm

Firm

profitsarerevenue, R, less total cost,

C

(the firmindex i is deleted forclarity). Total

cost consists offixed cost

Cf

plus variable costs Cy:

7i

=

R-(Cf

+

Cv). (12)

Because

ittakestimetoprocess

and

fillorders, the priceoftheproduct

may

change between

the

time

customers

placean order

and

receive the product.

We

assume

customers

pay

theprice in

average value

each

orderinthe backlog.

The

average value of

each

orderinthe

backlog

is thetotal

value oftheorder book,

V.

divided

by

the

number

ofunits

on

order:

R

=

Q(V/B).

(13)

The

valueoftheorder

backlog accumulates

the valueof

new

orders lessthe revenues received for

ordersshipped:

V

=

l(PO-R)dt

+

Vo. (14)

Fixed

costs

depend on

unit fixedcosts, Uf,

and

current capacity, K; variablecosts

depend on

unit

variablecosts, Uy,

and

production,

Q.

Both

fixed

and

variable costsper unit fallas cumulative

production experience, E, grows, accordingto a standardlearning curve.

Thus

Cf=UfK

(15)

Cv =

UvQ

" (16)

Uf-Ufo(E/Eo)T^

(17)

Uv

=

_Uvo(E/E())y (18)

E

= lQdt + Eo

(19)

where

_Ufo

_{and Uvo}

are the initialvalues

of

unit fixed

and

variablecosts, respectively,

Eq

isthe

initial level of production experience

and

y

is the strengthofthe learning curve.

For

simplicity

we

assume

the firm maintains

no

inventories

and

makes

all productto

order."

Shipments

thusequal production,

which

is the

minimum

ofdesired production,Q',

_and

capacity, K. Desired production is given

by

thebacklog, B,

and

thetargetdeliverydelay x*.

Backlog accumulates

orders,

O,

less production:

Q

=

MIN(Q*,

K). (20)

Q*

=

B/x*

(21)

B

=

_J(0

-

_Q)dt

+ Bo

₍₂₂₎

Capacity adjuststothetarget level

K* with an

average lagX. Specifically,

we

assume

K

adjusts to

K'

with athird-orderErlang lag, corresponding wellto the distributed lagestimated in investment

function research (Jorgenson

and Stephenson

1967):

where

£

is theErlanglag operator.

For

simplicity the lagis

symmetric

forthecasesofincreasing

and

decreasingcapacity.

Firm

Strategy

Under

thetraditional

assumptions

ofperfect rationality

and

equilibrium,

each

firm's target

capacity

and

pricing behavior

would

be given

by

thesolutiontothedifferential

game

defined

by

the

physical

and

institutional structureofthe

market

presentedabove.

However,

in reality firms

do

not

determine theirbehavior

by

solving

dynamic programming

problems

of

such

complexity

(e.g.

Camerer

1990, 1991).

Business

schools

do

notteach future

managers

how

to formulate

and

solve

dynamic

programming

problems

when

setting strategy. Rather, firms use intendedly rational

heu-risticstoset prices

and

acquirecapacity,

and

the analytic

models

intheliteraturereachthe

managerial audience in the

form

ofrules of

thumb.

In thecaseofthelearning curve,

books and

consultants prescribe rules

such

as

"By

slashing prices

below

costs,

winning

the biggest share

of

industry

volume,

and

acceleratingits cost erosion,a

company

[can] get

permanently

ahead

ofthe

pack...[and build] an unchallengeable long-termcost

advantage"

(Rothschild 1990, 181). hi this

spirit,

we

model

target capacity

and

price withrealistic

boundedly

rational heuristics,heuristics

which

allow us to capturedifferent strategiesfor

managing

the productlifecycle

and

learning

curve, including the 'marketshareadvantage leadsto

lower

costs leads togreater

market

share

advantage' logic derived

from

the analytic literature. Inparticular,

we

assume

the firm forecasts

future

market

demand

and

then determines

what

shareofthat

demand

it

would

liketo

command.

Target capacity therefore consistsofthe product ofthe firm's target

market

share, S*,

and

its

forecast ofindustry

demand,

D'^,adjusted

by

the

normal

rateofcapacity utilization u':

K*

-

MAX[K"'",

S*D7u*]

(24)

where K"""

is the

minimum

efficientscaleofproduction.

Because

ofthe capacity acquisitiondelay the firm

must

forecast

demand

A.yearsahead.

We

assume

firms forecast

by

extrapolating recent trends in

observed

industry

demand

(CoUopy

and

orderrate,

D^

aivdexponentially extrapolate the recent

growth

in industry orders,

_g^

over

the

forecasthorizon X^:

D'

=

D'EXP(?ifg')

(25)

d(D')/dt

= (O

- _{D'Vx" (26)}

g'

=

ln(D',/D',.;,.)/?i^ (27)

where

X^isthe historical horizon

used

to

compute

theexpected

growth

rate in

demand

G^.

The

instantaneous, currentvalueofindustry ordersis not availableto firms

because

ittakes time to

collect

and

report the data,so the forecast is

based

on

the reported orderrate, given here

by

first-order exponential

smoothing

ofactual industryorders with a

smoothing

time ofx^

(Sterman 1987

provides empirical evidence consistentwith

such

forecastingprocedures forbothlong-term

energy

demand

forecasts

and

short-terminflation forecasts).

The

firm's target

market

share, S*,

depends

on

its strategy.

We

consider

two

strategies,

'aggressive'

and

'conservative'. In the aggressive strategy,the firm followsthe

recommendation

ofthe learningcurveliterature

by

seeking a

market

share large

enough

to

move

thefirm

down

its

learningcurve fasterthan its rivals. Incontrast, the conservative firmseeks

accommodation

with

its rivals

and

sets a

modest market

share goal.

We

also

assume

firms

monitor

theactions oftheircompetitors.

The

aggressive strategy

seekstoexploit the learningcurve notonly

by

setting

an

aggressive

market

share goal but also

by

taking advantage offimidity, delayorunderforecasting

on

the partofits rivals

by

opportunisfically

increasing itstarget

when

itdetects sufficient uncontested

demand.

The

conservativestrategy

seeks

accommodation

withits rivals, butfears overcapacity

and

will cede addifional shareto avoid

it.

Thus

targetshare is given

by

{

MAX(S""",

S") ifStrategy

=

Aggressive

S*

=

<

(28)

^j^^gmax

gu^

jj:_Strategy

=

Conservative

where

S"^'"

and

S"'''"are the

minimum

and

maximum

acceptable

market

share levels forthe

expectsto

be

uncontested.

Expected

uncontested

demand

is the difference

between

the firm's

forecast ofindustry

demand

and

theirforecastof competitorcapacity.

Expected

uncontested

market

shareis given

by

theexpected uncontested

demand,

D", as afractionoftheprojected

industry

demand:

S"

=

MAX(0,

D"/D'). (29)

The

MAX

function maintains nonnegativity forS"

even

when

thereis excessindustry capacity.

Expected

uncontested

demand

is thefirm's forecastofindustry

demand

lessthe

sum

ofthe

fmn's

estimatesofexpected competitorcapacity, K*^, adjusted

by

the

normal

capacity utilization rate u*:

D"

=

D'

- _{u*Sj K'j,} j^i. (30)

In the basecase

we

make

thestrong

assumption

that firms accurately

monitor

theircompetitor's

capacity plans.

However,

we

assume

there is ashortdelay ofx'^ years required forthe firmto

carryoutthecompetitive intelligencerequiredtoestimate thecompetitor's targetcapacity

(exponential

smoothing

isassumed), soexpected competitor capacity

K^

evolvesas:

d(K'j)/dt

=

(K*j - K'j)/x'. (31)

To

model

the price decision,

we

assume

that

due

toadministrative

and

decision

making

lags, price, P. adjusts toa targetlevel P*, with an adjustment time x'':

dP/dt

=

(P* - _{P)/x^ (32)}

The

pricesetting rule

assumes

the firmdoesnot

have

theabilitytodeterminethe optimalprice

and

instead

must

searchfor anappropriate price level.

We

assume

firms usethe anchoring

and

adjustmentheuristic to

form

thetarget price.

The

current price

forms

theanchor,

which

is then

adjustedin responsetoconsiderationsofcost,

demand/supply

balance,

and market

share,

forming

a hill-climbingheuristic in

which

thefirm searchesforbetterpricesin the

neighborhood

ofthe

currentprice, usingcosts,

demand/supply

balance,

and market

share toassess the gradient.

For

simplicity

we

assume

the target priceis a multiplicativelyseparable functionofthe various

adjustment factors,

and

that

each

adjustmentis linear inthe input variables. Finally,thefurnwill

neverprice

below

unit variable costU^,.

Thus

a'

>

0;

a'

>

0; a'

<

0. (33)

The

threeadjustment terms capturethe firm'sresponse to unit costs, the

adequacy

ofits

capacity to

meet

demand, and

its

market

sharerelativetoits target share.

The

adjustment

parameters

a

determine thesensitivity ofpriceto

each

adjustmentpressure.

The

firstterm, the

adjustment forunit costs,

moves

target price

towards

a base price P*^ given

by

unitcosts

and

the

normal

profit

margin

m*:

P^

=

(l+m*)(Uv

+Uf).

(34)

The

firmalso respondstothe

adequacy of

itscurrent capacity,

measured by

thedesiredrate

of production

Q*

divided

by

'normal production', definedas theproduction rate given

by

current

capacity

and

the

normal

capacityutilization fraction u*.

When

this ratio

exceeds

unity, thefirm has

insufficientcapacity

and

increases price

above

the current level;excess capacity creates pressure to

lower

price.

Finally, thefirm attempts topricestrategically insupportofitscapacity goals

by

adjusting

prices

when

thereisa

gap

between

itstarget

market

share S*

and

its current shareS.

When

the

firmfinds itdesiresa greater share than itcurrently

commands,

itwill

lower

price; converselyif

market

share

exceeds

itstarget itwillincrease price,trading off theexcess

market

share for higher

profits

and

signalingrivals its desiretoachieve a cooperativeequilibrium.

The

price formulationis consistent withthe behavioral

model

ofpriceinCyert

and

March

(1963/1992), experimental evidence

(Kampmann

1992),

and econometric

evidence

from

a similar

model

ofinterest rate settingbehavior (Hines 1987). Paich

and

Sterman

(1993) createdaproduct

lifecycle simulation

microworld

similartothepresent

model

as

an

experimental system,

and

estimatedasimilar

model

forpricing

which

capturedthepricingbehavior ofthesubjects well.'

4.

Results

We

begin

by

confirmingthat

under

condifionsofperfect foresight

and

instantaneous

market

clearing the

model

reproducesthe conclusions oftheexisting literature.

We

then explorethe

effectivenessofthelearningcurve strategy asthese

assumptions

aregradually relaxed

by

exploring

For

thebase case the

model

is calibratedtocapture the

dynamics of

typical

consumer

electronics items suchas

camcorders

(table 1).

As

scalingparameters

we

setthe initial priceat

$1000/unit,

and

thepotential size ofthe

market

at the initial priceto

60

millionhouseholds,

each

seeking[i

=

1 unit.

The

product is

assumed

tobe durable, with a

10%/year

replacementrate.

We

assume

a

70%

learningcurve (costsfall

30%

for

each

doubling of cumulativeproduction), a

typical value fora

wide

range ofproducts.

The

ratiooffixedto variable costs is 3:1.

The

sensitivityof ordersharetoprice is high(Ep

-

-8),

implying

products areonly

moderately

differentiated

by

non-price factors, an

a

fortiori

assumption

thatfavors the effectiveness ofthe

learning curve strategy.

We

assume

short delaysof only

one

quarteryearforthe reportingof

industry orders

and

theestimation ofcompetitortarget capacity. Ingeneral these parameters favor

thesuccess ofa learning curve strategy

(we

presentsensitivity analysis below).

We

examine

the behaviorofthe

market

forvaluesofthe

word

of

mouth

parameter .5

<

(3

<

2.5. This range generates product lifecycle

dynamics

that

span

much

ofthe variation in

observed

diffusion rates (Parker 1994,

Klepper

and

Graddy

1990).

For

illustration,

we

define three

scenarios fortheevolution ofindustry

demand:

Fa.st,

Medium,

and Slow,

defined

by

valuesof(3

=

2, 1,

and

.5, respectively. Figure 1

shows

theevolution ofthe industryorder rate generated

by

the

demand

sectorofthe

model

for

each

scenario,

assuming no

capacity constraints

and assuming

that

prices follow unitcosts

down

the learningcurve (the target

market

shares forboth firms

=

.5). All

exhibit aperiodofrapid

growth

followed

by

a

peak and

decline tothe equilibrium,replacement rate

of

demand.

The

stronger the

word

of

mouth

feedback,the greater the

dynamic

complexity

ofthe

market: thefaster thegrowth, the earlier

and

higherthe

peak

rate oforders,

and

the larger the

decline

from peak

toequilibrium

demand.

Demand

in the

slow

scenario

peaks

afterabout

20

years,while in thefast scenario, the

peak

comes

atabout year6.

Even

faster

dynamics have been

documented, such

as black

and

whitetelevisions, calculators,

and

many

toys

and games,

often

with only

a few

years

from

boom

tobust.

For each

ofthethree

market

scenarios identified

above

we

testthe effectiveness ofthe

parameters

and

initial conditions, sotheplayingfield is level.

Only

the strategy

each

uses for

capacity planning

and

pricing

may

differ.

Note

in particularthatthe forecastingprocedure used

by

each

firm is identical,sothe

two

fimis

have

consistent beliefs aboutindustry

demand

and

competitorcapacity. In theaggressive strategy, thefirm seeks at least

80%

ofthe market, large

enough

toprovidethefirm withasignificant advantage incumulative production

and

drive the

learning curvein its favoryet not so large as to invite antitrust action (theaggressive playerwill

increase its

market

sharegoal

above

80%

ifitperceivesthere is additional uncontested

demand).

The

conservative playeris willingtosplit the

market

withits rival, but will

cede

ifitperceivesa

50%

share

would

result inexcesscapacity.

To

test

whether

the

model

reflectsthe competitive

dynamics

analyzed inthe existing

literature,

we

begin

by

assuming

that capacitycan instantly adjusttothe level requiredtoprovide

thetarget rate ofcapacityutilizationat alltimes:

K

=

Q7u*.

(23')

The

'perfect capacity' case correspondstotheequilibrium

assumption

thatthe

market

always

clears,either

because

capacitycan

be

adjusted instantly, or

because

agents

have

rafional

exf)ectations

and

perfect foresight sothattheycan perfectly anticipate the capacity acquisition lag.

The

market always

clearswith

no

unintended

backlog

accumulations,

and

capacity utilization

always

equalsthe target rate. Pricesthus

respond

onlyto unit costs

and

the

gap between

the firm's

target

and

actual

market

share.

The

price rule yieldsbehaviorconsistent with the

recommendations

intheliterature: the aggressiveplayerwill respondtotheinitial

gap between

target

and

actual

market

share

by

reducingprice

below

the short-termequilibrium.

Table

2

shows

discounted cumulativeprofits forthe three

market

scenarios.

(Throughout

thepaper

we

use a discountrateof

4%/year and

simulate the

model

for

40

years.

The

results are

robust to rates

from

toat least20%/year.) In allcases theresult is a prisoner's

dilemma.

Even

though

the payofftothe cooperative,conservative strategy [C,C]

maximizes

the net presentvalue

of cumulativeprofit forboththeindividual firms

and

the industry,

each

player has astrategic

continue toplay theconservativestrategy.

However,

afirmthat finds itselfplaying conservative

while the otherpursuesthe learningcurve strategy

would

improve

theirposition

by

defecting, so

[A,

A]

is the

dominant

strategy. Aggressivelyexploiting the learningcurve is the

dominant

strategyiffirms

must

irrevocably

and

independently

choose

theirstrategy atthebeginning ofthe

industry, ifthefirmcancredibly

commit

totheaggressive strategy

and

persuade its rival to

acquiesce, orifthefirst

mover

gains sufficient

advantage

before rivals

can

respond.

The

fasterthe

dynamics

ofthe

market

unfold, the greaterindustry profits are for

any

strategy

combination

(figure

2

shows

the relativepayoffsinthe

market

clearingcaseas functions

of

the

word

of

mouth

parameter

[3). Stronger

word

of

mouth

bringspeople intothe

market

sooner,

hence

boosting cumulative profit. Consistent with Kalish(1983), the

advantage

oftheaggressive

strategy,

and

thus thestrategic incentivetodefect, increaseswiththespeed oftheproduct lifecycle.

Similarly, sensitivityanalysis

shows

thatthe stronger the learning curve, the greateris thestrategic

incentivetoplay theaggressive strategy.

These

results

show

the

model

conforms

tothegame-theoretic result

when

we

assume

instantaneous

and

perfect capacityadjustment.

An

appropriablelearningcurve

makes

it optimalto

expand

capacity

and

price

below

the short-run profit

maximizing

level.

The

stronger the learning

curve, the greater the incentive topursuetheaggressivestrategy. Likewise, thefasterthe

growth

ofthe market, thegreateris the

advantage

ofthe aggressivestrategy.

We

now

examine

thecase

where

thefirm faces thecapacityadjustmentlag

and must

therefore forecast industry

demand

and

competitorresponses, as specified

by

thebehavioral rules

inequations 23-34. Figure 3

shows

thepayoffsasthey

depend on

the

word

of

mouth

parameter;

table 3

shows

the payoff matricesforthe different scenarios.

The

capacity adjustmentlag

and

behavioral decision rulesdramaticallyalterthepayoffstothe different strategies.

As

longas the

market

dynamics

aresufficiently slow, the firm's capacity forecasts are accurate

enough

and

the

aggressive strategydominates.

However,

for

market

dynamics

fasterthan those given

by

acritical

value ofthe

word

of

mouth

parameter, _P*^'^^=1.3, theconservative strategy

dominates

the

incentivetodefect,

and

[C,

C]

becomes

the unique

Nash

equiUbrium.

Note

thepenalty

imposed

when

both firmsplaythe aggressive strategy is

much

greaterthan in the

market

clearing case.

To

identify

why

the payoffs

change

so dramatically

when

theequilibrium

and

perfect

foresight

assumptions

are relaxed, figure

4a

shows

the

dynamics

ofthe [A,

C]

case forthe fast

market

scenario, while figure

4b shows

the

same

scenario forthecase

where

capacity adjusts

instantaneously. In bothcases,the aggressive firm

immediately

perceives a

gap between

its initial

share of

50%

and

its goal of

80%,

and

cuts price, hi thecase withthe capacity lag, theaggressive

firmalsosets target capacityto

80%

ofits forecast ofindustry

demand.

The

demand

forecast

extrapolates the rapidly risingindustry orderrate. Afterabout

one

year, thefirmexpectsindustry

demand

to

grow

ata rate inexcess of 100%/year, causingtarget capacity toincrease well

above

the

firm's currentcapacity requirements

and

swellingthe supplyline ofcapacity

on

order.

Due

to the

capacityacquisifion lag

and

thedelay in perceiving industry orders,bothfirmsreach full capacity

utilization afterabout .5years. Capacity

remains

inadequate until year about 1.5.

During

this

time, excessbacklogs

accumulate

and customers

are forcedto wait longer than

normal

fordelivery.

The

capacity

crunch

causes bothfirmstoboostprices

above normal

levels,

though

theaggressive

firmcontinues toprice

below

theconservative firm.

Such

transient price bubbles are often

observed

during the

growth

phases of highly successful products, as occurredfor

example

with

radios,black

and

white television,

and

colortelevisions

(Dino

1985)

and

more

recentlywith 1

Mbit

DRAM

chips

and Harley-Davidson

motorcycles.

Beginning

in about year2,

and

acceleratingdramaticallyafterabout year4,the market,

though

growing, experiences a decline in the fractional

growth

rate.

As

thedataare reported, the

firm lowersits forecast

of

future

growth

rates, but

due

to the lagsin thereporting ofindustry

orders, inassessingthe

growth

rate

from

historicalorderrates,

and

in adjustingcapacity tothe

target, actualcapacitybegins toovershoottherequiredlevel,

and

capacityutilization falls

below

normal.

As

industry orders

peak and

decline, shortlybefore year6, both firmsfind theirforecasts

have

gone

badly

wrong,

leaving

them

with excesscapacity.

The

aggressive firmsuffersthe most,

duringthe

same

period

been growing

atanadditional ratetoincrease its

market

share (notethatthe

aggressor's capacity

peaks

lateraswell as higher than thatoftheconservative firm).

As

boom

becomes

bust, theaggressive fimi finds capacity utilization drops

below

50%. The

conservative

firmalsoexperiencesexcess capacity, butthe

magnitude and

duration ofthe

problem

is

signifi-cantlylesssince theconservative player has

been

steadilygiving

up market

shareduringthe

growth

phase, partially offsettingits excessivelyoptimistic forecasts.

The

patternofcapacity

overshootis

widespread

in

maturing

industries (Porter 1980),

and

was

frequently

observed

in

Paich

and

Sterman's (1993) experimental product lifecycle task,

even

when

subjects

had

experi-ence

with thedynamics.

As

aresultoftheexcesscapacity generated

by

the saturationofthe

market,both firmsexperiencea periodoflosses as revenues

drop

below

fixedcosts.

The

losses

oftheaggressive firm,

however,

are substantially largerthan those oftheconservative firm.

The

aggressor generates a net lossof

more

than

$2

billionperyearas industry sales

peak around

year

6.

Though

the aggressive firm earns superiorprofits afteryear8 these fail to

compensate

forits

earlier losses, leavingitwith discounted cumulative profits of-$1.7billion

by

year40.

The

failureoftheaggressivestrategy

when

the

market

dynamics

are rapid isnot

due

tothe

failureofthe learning curvetoconfercost advantage

on

theaggressive firm.

As

inthe perfect

capacity case, the aggressive strategyachieves its intended goal:

low

prices

and

rapid

expansion

quickly givethe aggressor acost

advantage

which

steadily

widens

as the industry

moves

through

its lifecycle. Indeed,at the

end

ofthe simulation, theaggressive firm has unitcostsonly

42%

as

great asits rival, a largeradvantage thanit

enjoyed

in the perfectcapacity case.

The

failureofthe

aggressivestrategy is

due

entirely tothe

combination

ofthe capacityadjustment lagwitha

bound-edlyrational forecastingheuristic.

When

capacity adjusts perfectly theaggressive strategy

always dominates

theconservative

strategy

and

faster

market

evolutionincreases the advantage oftheaggressive strategy(figure 2).

Incontrast,

when

firms facea capacity adjustmentlag, the costs

of

excess capacity

induced

by

forecast error increase withthe speed oftheproductlifecycle. Eventually,the costs of excess

inferior(figure 3).

As

the

dynamic

complexity

ofthe

market

environment

grows, oras the

capacity acquisition lag increases, the likelihoodofsignificant capacity overshoot grows,

and

an

aggressive strategy

becomes

significantly lessprofitable than theconservative strategy

even

if

a

firmis ableto

commit

to an aggressivestrategysecure inthe

knowledge

thatits rivalwillcede.

Sensitivity

Analysis

Before

drawing

any

general conclusions

from

theresultsitis importanttoexplorethe

degree to

which

they are sensitive toassumptions. Despitesubstantial variationsin

key

parameters

(table 4),the critical valueofthe

word

of

mouth

parameter

above

which

thelearning curve strategy

becomes

inferior, _P^"^'^,

remains

inthe range

from

2.0to lessthan .5,

corresponding

to sales

peaks

from

five to

twenty

years afterproduct launch, well withintherange

documented

for

numerous

real products (Parker 1994).

We

have

made

a

number

of

assumptions

thatreducethe attractiveness of

a

learningcurve

strategy. First,to theextent capacitycan be

used

to

make

follow

on

productsthe costsofcapacity

overshoot will

be

mitigated.

Second,

we

assume

there are

no

economies

of

scope

allowing

follow-on or related products toshare inthe benefitsoflearning.

To

the extent learning

can be

passed

on

toother products,thereby conferring

advantage

to them, the costsof capacity overshoot

are offset

even

ifcapacity is not fungible with successorproducts. Third,

we

assume

there are

no

returnsto scaleor other positive

feedback

processes

such

as

network

externalities. Additional

positive feedbacksor other sources of increasingreturns favortheaggressorjustas a stronger

learningcurve increases the

advantage

ofthe aggressive strategy (seee.g.

Arthur

1989). Fourth,

we

assume

thereis

no

growth

in the underiying poolofpotential customers. This too

would

reducethe severity ofthe saturation peak. Fifth,

we

assume

a durable product.

More

frequent

repurchasesreducesthe

dynamic

complexity

ofthe

market

and

the

magnitude

ofthe decline

from

peak

toreplacement sales rates.

One

ofour

key

behavioral

assumptions

is that firms forecastindustry

demand

by

extrapolating past

demand

and have

no

advance

knowledge

ofthe market'ssaturation point. In the

saturation. Clearly, betterforecasting

would

favortheaggressivelearning curve strategy, as

shown by

theresultsofthe

market

clearing case.

The

evidence

is notencouraging. InPaich

and

Sterman's (1993) experimental version ofthe present

model,

subjects consistently failed to forecast

thesalespeak, leadingtoexcesscapacity

and

large losses similartothosesimulatedhere

- even

afterextensiveexperience with the task. Outsidethe laboratory,a

wide

range of

new

product

diffusion

models have been developed

which, in principle, allow forecastingofthe sales

peak

(Parker

1994 and

Mahajan

etal.

1990

reviewtheextensive literature). In practice,diffusion

models

oftenmiss the turning point as well, since,as

Mahajan

etal. (1990) write,

"by

thetime

sufficientobservations

have

developed

for reliableestimation, it istoo latetousethe estimates for

forecastingpurposes."

Rao

(1985)

examined

theability

often

popular

models

to predictsalesof

typical durable goods.

Mean

absolutepercent forecast errorsaveraged

more

than

40%

across all

models and

products.

The

extrapolative

models

generally

outperformed

thediffusion models.

On

theother

hand

a

number

ofour

assumptions

tendto increase theadvantage of an

aggressive strategy.

We

assume

learning is perfectly appropriable, increasing theabilityoffirmsto

gain sustained cost advantage.

We

assume

market

shareis quiteelastic sothat

modestly lower

pricesbring significant share advantage, strengthening thepositive feedbacks created

by

the

learn-ing curve.

We

also

assume

that productionadjusts instantaneously atconstant marginalcost (until

capacity utilization reaches

100%), and

that capacitycan beadjusted continuouslywith an average

lagofjust

one

year, lessthan the typical lagsestimatedin theliterature.

There

are

no

capacity

adjustmentcostsorexit costs.

A

longer capacity lagor

more

realistic adjustmentcosts

would

sig-nificantly increase the

magnitude

and

cost offorecasterrors.

We

omit

balancesheetconsiderations

and

thus the risk of bankruptcy: aggressive firmsthatultimately

do

well

might

notsurvive the

lossesofthetransition

from

boom

tobust,again favoringthe aggressive strategy.

The

information

on

which

the firm bases its decisions is free ofnoise,

measurement

error, bias, or otherdistortion.

We

assume

firms

can

base their forecasts

on

industry orders,reported with onlya

one

-quarteryear

lag,

when

in

most

industriesorderdata are unavailable

and

firms

must

rely

on

estimatesofindustry

demand

(orders) withcapacity

(which

may

constrain

shipments

below

therateof

incoming

orders

during periods ofrapid

demand

growth).

Most

importantly,

we

assume

thatthecompetitor's

planned

capacitytargetis fully

known

with onlya short delay.

Relaxing

any

ofthese

assumptions

strengthensourresults

and

causestheaggressive strategyto

be

dominated

by

theconservative

strategy at

lower

ratesof

market

growth and

for lessdurable products.

The

assumption

thatfirms

know

their rivals'

planned

capacity levels bears closer

examination. Extensive experimental studies

(Sterman

1989a, 1989b, Paich

and

Sterman

1993,

Diehl

and Sterman

1995,

Kampmann

1992)

show

ina

wide

range ofexp)erimental markets that

people ignore or give insufficient

weight

tothe supply line of

pending

capacity or production.

The

tendency

toignorethesupply line (and

more

generally, failing toaccount fordelays,e.g. Brehm.er

1992) isrobust: itoccurs

even

in settings

where

thecontents

of

thesupply lineare available

costlessly

and

atall times, are

prominently

displayed,

and

are highlydiagnostic,

and

where

subjects

had

financial incentives to

perform

well. Failuretoaccount fortime delays

and

supply

lines appearstobe

common

in real

markets

as well. Studies

show

few

real estatedevelopers, for

example,

takeaccountofthe supplyline ofprojects

under

development

(Thornton 1992,

Bakken

1993), leadingtoperiodic overbuilding. Figure5

shows

the payoffs inthecase

where

we

assume

firms

do

notaccount forthesupply lineof

pending

capacity but instead usethecompetitors'

current capacity to estimate uncontested

demand:

K'j

=

Kj. (31')

When

thesupplyline is ignoredtheaggressive strategyis inferiorforall the

market environments

tested. Ignoringthesupply lineensuresthatduringthe

growth

phase

each

firmerroneously

believesits rivalis

expanding

capacity

much

less thanit actually is,

and

overestimates uncontested

demand.

The

aggressive playeropportunisticallyincreases its targetcapacitystillfurther

and

the

conservative playerfailsto

cede

sufficiently, leadingtoa

much

largerovershootofcapacity

and

much

larger losses

when

the

market

saturates.

The

aggressive strategy is

dominated

by

the

conservative strategy

even

inthe

slow

scenario

where

demand

forthe product

peaks

20

yearsafter

5.

Discussion

and

Conclusions

Priorresearch has

shown

that

under

assumptions

of equilibrium

and

perfect rationality, the

optimal strategy fora firmfacing a learning curveis toaggressively

preempt

competitors, cutting

price

and

boosting output

beyond

the static

optimum

levels.

We

have

shown

that

under

a

more

realistic set

of

assumptions,thenormative result

can

be reversed.

When

there arecapacity

adjustment lags,

commonly

usedforecasting heuristics leadtocapacity overshootas a

market

saturates. Investingin additional capacity

and lower

prices to achievelearning benefitsisonly

optimal

when

the

dynamic

complexity ofthemarket,

and hence

the riskofcapacityovershoot, is

low. In thesecircumstances fully

and

boundedly

rationaldecision

making

converge.

However,

as

the

dynamic

complexity

ofthe

market

increases,disequilibriumeffects

and

systematicdecision

making

errors

become

more

important,

and

cause the predictions oftherational

model

to fail.

These

conclusions are consistentwith experimental

and

empirical evidence.

The

results

predictthatlearningcurvestrategies will

perform

bestinindustries

where

there is

slow

demand

growth

(or

where

customer awareness

ofthe product category is alreadyhigh),theproduct has a

highrepeatpurchaserate

and

is fairly undifferentiated,or

where

capacitycan beadjusted rapidly at

low

cost. Observationsthat learningcurve strategiesgenerally led tosustainedadvantage in

industries

such

as synthetic fibers, bulk chemicals,

and

disposable diapers

(Shaw

and

Shaw

1984,

Porter 1984,

Lieberman

1984,

and

Ghemawat

1984

respectively) arebroadly consistentwiththis

prediction. Similarly, ourresultspredict

poor

performance

foraggressive strategies in industries

with high

word

of

mouth,

durable, differentiated products, orlong capacity adjustmentdelays.

The

overcapacity,excess inventory,

and

price

wars observed

in industries

such

as televisions

and

VCRs,

toys

and games,

lighting

equipment,

snowmobiles,

hand

calculators,tennis

equipment,

bicycles, chain saws, semiconductors,

and running

shoes citedearliersupport thisproposition.

The

results

have

implicationsboth forpracticing

managers and

forthe larger issueofthe

modeling

tools

most

appropriate for the study ofstrategicbehavior.

The

recommendation

to

pursue alearningcurve strategy

must always be

treated withcaution. Currenttexts

and

theory

recommend

aggressive

preemption

inthepresence ofstrong, appropriable learning curvesor other

positivefeedbacks thatconferincreasingreturns.

Our

results

show

thatfirms

must

also determine

whether

they are vulnerabletocapacityovershoot orunderestimationof competitorcapacityplans.

A

firmelectingtopursue a learningcurve driven strategy

must

devotesignificant effort to

understandingthe

dynamics

of

market

demand

sothatitisnotcaught

unprepared

by

market

satu-ration. It

must

clearly

and

credibly signalits capacity intentionsina rapidly

growing market

sothat

lessaggressiveplayers will not unintentionally overbuild.

To

prevent competitoroverbuilding, it

may

find itoptimal toshareits forecasts

and market

intelligencewithrivals.

Experience

and

experimentalstudies suggestthat thisisboth hard

medicine

totake

and

difficulttocarry out

successfully. Rather,it appearsthat

when

high

dynamic

complexity

increases the riskofcapacity

overshoot, firms should consider conservative strategies

even

inthe presence oflearningcurves

and

othersources ofincreasingreturns,allowinglesssensible rivals to play theaggressive

strat-egy, then

buying

these rivalsatdistress prices

when

theyfail duringthe transition

from

boom

to

bust.

Jack

Tramiel

followedjust

such

astrategy, purchasingAtari

from

Warner Communications

afterthe

peak

inthevideo

game

market

for

$160

million in

unsecured

debt

and

no

cash,while

Warner

took a

$592

millionwriteoffofAtari assets

on

topof

$532

million in Atari losses.

On

the methodologicalfront, ourresultssuggest thattheequilibrium

and

rationality

assumptions

of

game

theory

and

microeconomics

arenot robust.

More

realisticphysical,

institutional

and

behavioral

assumptions

can reverse the neoclassical result

and

reveals a

much

more complex

relation

between

thelearning curve, the

dynamics

of

demand

and

firmstrategy.

When

the

system

dynamics

are sufficiently slow, the delaysin informationacquisirion,

decision

making

and system

response sufficiently short,

and

the cognitive

demands on

theagents

sufficiently low, behavioraltheorieswill yield predictions observationally indistinguishable

from

thoseof equilibrium models.

However,

incases of high

dynamic

complexity,

boundedly

rational

peoplecan

and

do

behave

significantly differently.

The

case ofthe learningcurve ina

dynamic

market

shows

these differences

can

matter greatly,

and

their

impact

can

be

examined

rigorously.

D-4354 22

differencesinavariety

of

other contexts.

Such

cases arelikelyto includesettings in

which

there

arelong time delays

between

action

and

effectorin the reportingofinformation,

where

there are

positive feedback processes (increasingreturns),

and

where

there are significant nonlinearities

(Stemian

1994,

Arthur

1994). Likely

examples

include markets such as shipbuilding, real estate,

paper,

and

many

others

plagued

by

chroniccyclicality,

and

industries with

network

externalities

and

standard formation issues

such

as

telecommunications

and

software.

We

suggestthe

combination

of

game

theoreticreasoningwith behavioralsimulation

models

can help createa

meaningful

'behavioral

game

theory'

(Camerer

1990, 1991),thatis, a behaviorallygrounded,

empirically testable,

and

normatively usefultheory of disequilibrium

dynamics

in strategic settings.

NOTES

1

The model

is solved

by

Eulerintegration withatimestepof .0625 years.

The

results are not

sensitivetothe use of smaller time stepsorhigher-orderintegration

methods.

2. Includinginventories

would

substantially destabilize the

system (Sterman

1989b); omitting

inventoriesisthus

an

a

fortioriassumption.

3. Paich

and

Sterman

(1993) estimatedaslightly different

form

ofthe

model,

in

which

there

was

no market

share effect.

They

found

the cost effect

was

very strong, whilethe response tothe

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