Dynamics of Competition Between
Incumbent and Emerging Network
Technologies
Youngmi Jin (Penn)
Soumya Sen (Penn)
Prof. Roch Guerin (Penn)
Prof. Kartik Hosanagar (Penn)
Prof. Zhi-Li Zhang (UMN)
1
Motivations

Success of new network designs depend not only on their technical
advantages, but also on economic factors

Many network technologies have initially failed to widely deploy
 Ex: IPv6, multicast, various QoS services.
 Relevant in the context of competing network solutions (Ex: IPv4 vs. IPv6) and
“clean slate” proposals for new Internet architectures (of NSF FIND).

Connectivity is a salient feature of network technologies.
User’s choice of the technology depends on the number of other users reachable
This network externality produces unique dynamics arising from the path
dependence and time sequence of the user adoption process
 Converters can provide connectivity across technologies and thus become
strategic tools to influence adoption levels



Requires models that provide a framework to analyze the dynamics of
competition between entrant and incumbent network technologies, and
their relative market penetration levels in the long run (equilibrium
outcome).
2
Related Areas

Adoption of Incompatible Technologies




New Product Diffusion




Considers static models
Shows that Network Externalities can lead to multiple equilibria and converters
can significantly impact equilibrium adoption levels.
Does not focus on modeling how the diffusion process selects one of several
equilibria
Most models provide insights on aggregate system dynamics
Some consider individual-level decisions but focus on single technology
adoption
Individual-level decision models for single technology is not applicable in
scenarios with a strong incumbent.
Our Objective is to develop a model that:


Allows us to understand both individual-level decision making and systemslevel dynamics in a two technology competition setting.
Accounts for how user choice for technology is affected by the relative intrinsic
merits of the competing technologies, individual user’s affinity for each of
them, network externality associated with subscription size, converter
efficiency and price.
3
Technology Adoption Model

User technology adoption model:


Utility functions combines user preference, technology quality, network externalities and
price :
 U1( ,x1) =  q1 + (x1 + α1 β x2 ) – p1
 U2( ,x2) =  q2 + (β x2 + α2 x1 )– p2
Basic parameters

 : individual user preference (uniformly distributed in [0,1])

qi: intrinsic benefit of technology i (qi >0)
 q2 > q1 (Entrant has a higher intrinsic quality than the incumbent)

xi: fraction of technology i adopters (0 xi 1, i=1,2; x1+ x21)
 Linear network externality (Metcalfe’s Law)
 α1 and α2 denote converter efficiencies

pi: price of technology i, i={1,2} (pi >0)
β captures the relative difference in the magnitude of network benefits of the two
technologies.
 Maximum network benefit derived by technology 1 adopters is normalized to one. All
benefits and costs are expressed in the same unit.


Conjoint Analysis can be used to estimate various parameters
4
Problem Definition

User’s choice (Rational and Incentive compatible decision process)
 Users adopt a technology only if they derive positive utility from it
 Users adopt the technology that provides the highest utility
no technolog y if

if
technology 1
technology 2 if


U i  0 for i  1,2
U1  0 and U1  U 2
U 2  0 and U 2  U1
Adoption indifference points 10 , 20 , 21
10 : U1 ( )  0 if   10 , users adopt tech nology 1
 20 : U 2 ( )  0 if    20 , users adopt tech nology 2
12 : U 2 ( )  U1 ( ) if    21 , users prefer tec hnology 2
p1   x1  1x2 
q1
p  x2   2 x1 
20  x   2
q2
p  p1  1  1 x1   1  1 x2
21  x   2
q2  q1
10  x  


Denote as Hi(x,t) the number of users who derive positive and higher surplus from
technology i than its competitor at time t (i=1,2), where x=(x1,x2)
 At equilibrium Hi(x*) = xi*, i=1,2

We need to characterize Hi(x,t), i=1,2, and their evolution over time
 Establish relation between Hi(x,t) and (technology) indifference points that
correspond to changes in user adoption decisions
 Derive explicit functional expressions for Hi(x,t)
 Specify (technology) adoption dynamics
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Problem Formulation

Characterizing Hi(x,t)
 
 
  21 0,1  10
H1  x   
0
 
 
0,1
if 10   21
otherwise
1   21 0,1 if 10   20
H 2 x   
0
1   2 0,1 otherwise

Diffusion dynamics:

Current adoption level at time t are announced to all users.
 Users learn about new levels and react to it at different times, hence the diffusion
is assumed to proceed at some constant rate γ<1.
 Users compute their surplus from the technologies and make their choice based
on the relative positions of the indifference points that determine the expression
of Hi(x(t)) to be used for the dynamics.
 Hi(x(t)) governs the evolution of the trajectory that result in new adoption levels,
affecting the positions of the indifference points which in turn determine the
expression for Hi(x(t)) to be used for further evolution of the diffusion trajectory.
dxi (t )
  H i  x(t )   xi (t ) , i  1,2
dt
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Solution Outline

Functional form for Hi(x) changes depending on the relative position of the
indifference points of technology adoption

We can have Nine different combinations of H1(x) and H2(x), each
corresponding to a different “region”.
 Each “region” boundary can be characterized

In each region we solve
 Hi(x*) = xi*, i = 1,2



dxi (t )
  H i  x(t )   xi (t ) , i  1,2
dt
Verify xi*, i = 1,2 belongs the corresponding region


H1(x)=1,
H2(x)=0
Formal characterization of the validity and stability conditions
p2-p1-(x2-x1)
H1(x)=
Identify the portion of the trajectory that lies in its associated
region, where
q2-q1 it
exits it, and connect trajectory segments together
p2-p1-(x2-x1)
H2(x)= 1-competition
Use to get insight into possible outcome behaviors of technology
q2-q1

Some representative examples to follow
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Preamble (1)

Entrant technology needs to consider carefully:

Sensitivity to price changes



Account for its growth rate relative to the Incumbent’s


Small variation in price can affect outcomes drastically
Stability characterization helps to improve understanding of sensitivity
Initial diffusion in the market is not predictive of eventual success
Technologies may coexist even in absence of converters.
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The Impact of Pricing – (1a)

Technology 2 prices itself out of
(eventual) existence
 Note that it does take off and
gain some fraction, but
technology 1 is still grows at a
faster rate and eventually wins
 Relative Growth rates
matter!

Outcome is independent of
initial technology 1 penetration
(single equilibrium case)
q1= 2.95, p1=
1.01
q2= 5.5, p2=
2.57
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The Impact of Pricing – (1b)

Technology 2 prices itself
competitively (p2= 2.55)

The two technologies
converge to unhappy
coexistence (roughly equal
market shares)


Coexistence is possible
even in absence of
converters
Outcome is again independent
of initial technology 1
penetration
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The Impact of Pricing – (1c)

Technology 2 prices itself to
win (p2= 2.54)

Technology 1 continues
growing for some time after the
introduction of technology 2,
but is eventually wiped out.
 Outcome is again independent
of initial technology 1
penetration

A full range of possible
outcomes



Sensitive
Either or both technology can
survive
When can initial penetration
affect the outcome?
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Preamble (2)

More complex behaviors arise when multiple equilibria exist:

Final equilibrium attained depends on the Incumbent’s initial market
penetration.


Important consideration for the entrant to make entry (introduction time)
decisions
Important to characterize:

The combinations of multiple equilibria that may exist together
 The ‘basins of attraction’ and their associated boundaries where the
system will stabilize.
 The initial penetration levels that produce different outcomes


We have formal characterization for these.
Example to illustrate interesting behaviors produced in presence of multiple
equilibria and the dependence of the outcome on the Incumbent’s initial
market penetration
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Impact of initial penetration

The outcome depends on
the initial penetration of the
cheaper technology
incumbent
technology





Above a threshold, both
Either
of the technology
can
technologies
end-up
survive.
coexisting and achieve full
market penetration
Technology 2 needs to enter
Below
the threshold
only the
the market
early to win.
better technology survives
Entrant’s entry time can have
significant impact on the
survival of the incumbent
q1= 2.95,
0.3, pp1=1=0.5
1.2
q2= 5.1,
9.6, p2= 2.55
5.2
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Conclusions

Interactions of competing technologies with network externalities
can give rise to a wide range of outcomes based on


Pricing, technology quality, level of penetration of the incumbent, etc.
Our model can help to:

Characterize systems level dynamics from the individual level decisions
with explicit characterization of:



Equilibria
Trajectories
Basins of attraction in cases with multiple equilbria

Explore how small changes in system parameters can affect individual
decisions and ultimately lead to very different outcomes

Provides a framework to develop insight of what to watch for or take into
account when assessing how to best introduce new network
technologies

We also have generalized results for our system in presence of
converters and identified interesting effect on outcomes
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Future Directions

Time-varying technology quality and price



It gets better and cheaper over time
Pricing that depends on the number of adopters
How does each technology react to maximize its chances of survivals and/or its
profit

Profit model and profit maximization strategies

Validation

Identify existing/ongoing deployment scenarios on which to try to apply this, i.e.,
examples of prices, costs, qualities, etc
Thank You!
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