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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)

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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).

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Related Areas Adoption of Incompatible Technologies

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

New Product Diffusion 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 systems-

level 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.

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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+ x21) 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

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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

Adoption indifference points

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)

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.

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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

Verify xi*, i = 1,2 belongs the corresponding region Formal characterization of the validity and stability conditions

Identify the portion of the trajectory that lies in its associated region, where it exits it, and connect trajectory segments together

Use to get insight into possible outcome behaviors of technology competition Some representative examples to follow

2,1,)()()(

itxtxHdt

tdxii

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H1(x)=1, H2(x)=0

p2-p1-(x2-x1)q2-q1

H1(x)=

p2-p1-(x2-x1)q2-q1

H2(x)= 1-

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Preamble (1)

Entrant technology needs to consider carefully: Sensitivity to price changes

Small variation in price can affect outcomes drastically Stability characterization helps to improve understanding of sensitivity

Account for its growth rate relative to the Incumbent’s 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

Above a threshold, both technologies end-up coexisting and achieve full market penetration

Below the threshold only the better technology survives

Entrant’s entry time can have significant impact on the survival of the incumbent q1= 0.3, p1= 0.5

q2= 9.6, p2= 5.2

The outcome depends on the initial penetration of the incumbent technology

Either of the technology can survive.

Technology 2 needs to enter the market early to win.

q1= 2.95, p1= 1.2q2= 5.1, p2= 2.55

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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!