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Network externalities
1. Network Externalities
• What is a network externality?
– When a person buys a good or service, he
becomes part of a network.
– Thus the network increases in size.
– The utility that people derive depends on the
size of the network.
– By joining I make everyone else in the network
better off.
2. Model of Network Externalities
• Demand for service depends on the size of
the network.
• Let Vi be consumer i’s maximum value for
the product.
• Consumer i will “join” the network if:
Price < f*Vi where f is the fraction of the
population that has “joined” the network.
3. Network Externalities, con’t
• Assume that all consumers are uniformly
distributed in terms of value from 0 to 100.
• Then the percentage of the population with
a value less than or equal to X is X/100 and
the percentage with a value greater is (1-
X/100).
• Order all consumers based on their values
from highest to lowest.
4. Network Externalities, con’t
• To determine total demand at any price we
need to find the “marginal” consumer, call
him j, who is indifferent between joining
the network and not joining it.
– For this consumer price = fVj.
• If this consumer is indifferent, all
consumers with higher values will join and
all consumers with lower values will not.
5. Network Externalities, con’t
• Since all consumers with higher values join,
f = 1 - Vj/100.
• Rewrite this to get Vj =100-100f =100(1-f).
• By definition of the marginal consumer, p =
f*Vj which we can now rewrite as:
p = f*100(1-f).
• This is an inverse demand curve and we can
graph it.
7. 0 1
f
p For all but the price
p’, there are two
“equilibria” -- one
with a low level of
adoption and one
with a high level.
p’
Flow Fhigh
8. Network Externalities, con’t
• Although there are two “equilibria” for each
price, the low price equilibrium is unstable
because any small increase in subscribers or
decrease in price will increase the number
of subscribers and move us to the high
equilibrium.
• So what price should the monopolist set?
9. Network Externalities, con’t
• Assume the market is a monopoly.
• Assume the MC of adding a subscriber is 0.
• Total profit = pfN = f100(1-f)fN = 100Nf2
-
100Nf3
.
• Take derivative of profit w.r.t. f (which the
monopolist controls indirectly through
price) to get 100N2f - 100N3f2
= 100N(2f-
3f2
).
• Setting equal to 0, we get that f =0 or f
=2/3.
10. Network Externalities, con’t
• Since f*=0 implies profits of 0, f* = 2/3
must be optimal.
• Of course, with different marginal costs, the
answer would be different.
• Since p = f 100 (1-f), p = 2/3*100(1/3)
=200/9 = 22.22.
11. Network Externalities, con’t
• So how does the monopolist get the
network started?
• Once the network gets started, consumers
with high values will buy, increasing the
size of the network, causing more
consumers to buy, causing the network to
grow, and so on.
• But no one wants to be the first to sign up.
12. Network Externalities, con’t
• Even for the consumer with the highest
value to want to buy, the network must be
of a certain minimum size f’ defined by p*
= f’100.
• Rewritten, f’ = p*/100 = 22.22/100 =
22.22%.
• Once the network gets to f’, the network
will grow until it reaches the equilibrium of
2/3.
13. Network Externalities and
Standardization
• With network externalities, there will be a few large
networks instead of several small ones.
• Will there be only one, or will there be competing
networks?
• Two factors to consider:
– With only one network, there is less product
differentiation, so competition will be more intense.
– But a larger network bestows more benefits on users, thus
increasing willingness to pay and price.
• Depending on which effect is larger, there are three
separate “games” which firms may play.
14. Tweedledum and Tweedledee
Firm 1
Tech. 1 Tech. 2
Firm 2 Tech. 1 3,3 6,7
Tech. 2 8,5 2,2
Network externalities are not very strong. Gains from adopting common
technology offset by intra-firm competition. Since neither NE is pareto
optimal, should expect a “battle” to see which technology will win.
15. Tweedledum and Tweedledee, con’t
• Types of possible battles to establish dominant
technology:
– Intense price competition to get the lead and the bigger
network.
– Attract suppliers of complements (software, games) to
increase consumer’s value of joining network.
– Product preannouncement to let people know what is
coming (Windows 95).
– Commitments to maintain low prices in the long run (cheap
upgrades).
• Results in these markets not predetermined, i.e. they
are path dependent.
16. Battle of the Sexes: Type 1
Firm 1
Tech. 1 Tech. 2
Firm 2 Tech. 1 10,10 5,4
Tech. 2 6,5 8,8
Network externalities are strong. Gains from adopting common
technology outweigh intra-firm competition. Since one NE is pareto
optimal, should have agreement on which technology will be the standard.
17. Battle of the Sexes: Type 2
Firm 1
Tech. 1 Tech. 2
Firm 2 Tech. 1 8,12 5,4
Tech. 2 6,5 10,7
Network externalities are strong. Gains from adopting common
technology outweigh intra-firm competition. Since neither NE is pareto
optimal, will have battle to determine the standard.
18. Pesky Little Brother
Firm 1
Tech. 1 Tech. 2
Firm 2 Tech. 1 12,4 16,2
Tech. 2 15,2 10,5
Firm 2 has an established dominant position in the industry and doesn't
want standardization. Smaller firm wants standardization -- wants to get
the benefits of Firm 2's network. No Nash Equilibrium.
19. Network Externalities and
Standardization, con’t
• If it is best that there is only one standard,
we can still have a problem as technology
changes.
• If a new technology is pareto superior, we
should switch to it.
• However, firms may not switch because
they fear being the only firm using an
incompatible technology.
21. Network Externalities and
Standardization, con’t
• On the other hand, it could be that the old
technology is pareto superior
• In this case, we may get excess momentum,
that is firms may switch because they fear
being the only firm not using the new
technology.
23. Network Externalities and
Standardization, con’t
• When introducing a technology, firms can
adopt an “evolutionary” or “revolutionary”
strategy.
– Evolutionary: Make the technology “backwards
compatible” so that people can easily switch
from an older technology to your technology.
– Revolutionary: Make the technology
“backwards incompatible”.
24. Network Externalities and
Standardization, con’t
• With two firms and two possible strategies,
get three types of “wars”.
– Rival Evolution: Both firms have new technologies that
are backward compatible, just not with each other.
(DVDs and Divx both play CDs but not each others’
disks.)
– Evolution vs. Revolution: One technology is backwards
compatible, the other is not.
– Rival Revolution: Both new technologies are
backwards incompatible. (Nintendo vs. Play Station.)
