Dynamics of Competition Between Incumbent and Emerging Network Technologies

1. 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)

2. 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 • 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.

3. Technology Adoption Model • User technology adoption model: • Utility functions combines user preference, technology quality, network externalities and price • Ui( ,xi) =  qi+ xi - pi, i = {1,2} • Utility functions in presence of converters: • U1( ,x1) =  q1+(x1 + α1 β x2 )–p1 • U2( ,x2) =  q2+(β x2 + α2 x1 )–p2 • 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 • 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) • α1andα2 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 decision) • Adoption indifference points • Denote as Hi(x,t) the number of users who derive positive and higher surplus from technology ithan its competitorat time t (i=1,2), where x=(x1,x2) • At equilibrium Hi(x*) = xi*, i=1,2 • We need to characterizeHi(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

5. 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)) • 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.

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

7. Impact of Pricing • 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.

8. Multiple equilibria cases • 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. • Examples illustrate interesting behaviors produced in presence of multiple equilibria and the dependence of the outcome on the Incumbent’s initial market penetration

9. 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 Future Directions Time-varying technology quality and price It gets better and cheaper over time 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 Conclusions