Network e ects
Week 6
Cabral Ch6 and EK Ch17
Introduction
De nitions
• Positive network e ects- more usage of the product by any user increases the product’s value for
other users
• Direct network e ects- increase in usage lead to direct increases in value
• Indirect network e ects- increase in usage of the product spawn the production of increasing
valuable complementary goods
• Two sided network e ects- increase in usage by one set of users increases the value of
complementary product to another distinct set of users e creditcardsshopsandcustomers
g
• Local network e ects- each consumer is in uenced directly by the decision of a typically small
subset of other consumers
• Unclenching network e ects- require agreement on standards that ensure compatibility
Modelling
NONETWORK EFFECTS
• Consumers are distributed over [0,1], and each want one unit of the good
• The good is o ered at price p* per unit
• Each agent has an intrinsic interest in the good, given by their reservation price, r(x)
• Arrange the consumers by decreasing reservation price
x's reservationpricer x
buys if notif
rap reap
If rlolpork
At equilibriumreset
p
scootbuythereisupwardpressure
if
if so x buythereisdownwardpressure
This issociallyoptimal
NETWORK EFFECTS
As well as intrinsic preferences, a consumer is also motivated by network e ects (due to positive
externalities)
Z fractionofthepopulationusingbuyingthegood
r self z reservation
price
t network
e ffect
assume i e aninc inusers
assume
reiko continuous z makesthegood
moreattractive
flolO
SI I l b
ff
, Selffulfillingequilibrium
Ifscexpectsztobuy.theybuyifr.beflz p
Selffulfillingexpectations predictz theninequilibrium zisthetractionthat
perfectly
agents willbuy
Equilibriaat
pitraft NBloweringpricenolongerraisesequilibriumdeman
ifptoogreat
o
lowerpmeanstippingpointis
EG r x plz z
lowertviability
pertzlelz r zf z z 1 z
mat 2 1 2 44 at 2 112
consumer
higher p ly p has3equilibriaat 2 0,212
I
confidence inthe
in
p ly equilibriaat 2 0
confidence
successor the the
successof
pong
zzz 2 z z z z
towards downward
downward upwardpressure
pressure
on
pressure
z towardsz
coincidence
za za Z z z
stable tippingpoints stable
mass
equilibria critical
Imperfectpredictions
supposeeveryone believeszwillbay.soxbuysifrbdflzls.is
i ncorrectly
Fraction buyers esucnthatrlelflzt.pt
of
orreel
1,1 Er
I gie
Eg rat x flat
below unstable
approaching z'from
approaching above stability
from
Dynamics of a population
A population may react to network e ects over time
Audience changes dynamically based on agents’ expectations in
each period
Assume that in each period people myopically expect the audience
size to be the same in the previous period
initiala udience zt glzt.it
zo
Week 6
Cabral Ch6 and EK Ch17
Introduction
De nitions
• Positive network e ects- more usage of the product by any user increases the product’s value for
other users
• Direct network e ects- increase in usage lead to direct increases in value
• Indirect network e ects- increase in usage of the product spawn the production of increasing
valuable complementary goods
• Two sided network e ects- increase in usage by one set of users increases the value of
complementary product to another distinct set of users e creditcardsshopsandcustomers
g
• Local network e ects- each consumer is in uenced directly by the decision of a typically small
subset of other consumers
• Unclenching network e ects- require agreement on standards that ensure compatibility
Modelling
NONETWORK EFFECTS
• Consumers are distributed over [0,1], and each want one unit of the good
• The good is o ered at price p* per unit
• Each agent has an intrinsic interest in the good, given by their reservation price, r(x)
• Arrange the consumers by decreasing reservation price
x's reservationpricer x
buys if notif
rap reap
If rlolpork
At equilibriumreset
p
scootbuythereisupwardpressure
if
if so x buythereisdownwardpressure
This issociallyoptimal
NETWORK EFFECTS
As well as intrinsic preferences, a consumer is also motivated by network e ects (due to positive
externalities)
Z fractionofthepopulationusingbuyingthegood
r self z reservation
price
t network
e ffect
assume i e aninc inusers
assume
reiko continuous z makesthegood
moreattractive
flolO
SI I l b
ff
, Selffulfillingequilibrium
Ifscexpectsztobuy.theybuyifr.beflz p
Selffulfillingexpectations predictz theninequilibrium zisthetractionthat
perfectly
agents willbuy
Equilibriaat
pitraft NBloweringpricenolongerraisesequilibriumdeman
ifptoogreat
o
lowerpmeanstippingpointis
EG r x plz z
lowertviability
pertzlelz r zf z z 1 z
mat 2 1 2 44 at 2 112
consumer
higher p ly p has3equilibriaat 2 0,212
I
confidence inthe
in
p ly equilibriaat 2 0
confidence
successor the the
successof
pong
zzz 2 z z z z
towards downward
downward upwardpressure
pressure
on
pressure
z towardsz
coincidence
za za Z z z
stable tippingpoints stable
mass
equilibria critical
Imperfectpredictions
supposeeveryone believeszwillbay.soxbuysifrbdflzls.is
i ncorrectly
Fraction buyers esucnthatrlelflzt.pt
of
orreel
1,1 Er
I gie
Eg rat x flat
below unstable
approaching z'from
approaching above stability
from
Dynamics of a population
A population may react to network e ects over time
Audience changes dynamically based on agents’ expectations in
each period
Assume that in each period people myopically expect the audience
size to be the same in the previous period
initiala udience zt glzt.it
zo
