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Network effects and embedded options: decision-making under uncertainty for network technology investments

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Abstract

The analysis of network effects in technology-based networks continues to be of significant managerial importance in e-commerce and traditional IS operations. Competitive strategy, economics and IS researchers share this interest, and have been exploring technology adoption, development and product launch contexts where understanding the issues is critical. This article examines settings involving countervailing and complementary network effects, which act as drivers of business value at several levels of analysis: the industry or market level, the firm or process level, the individual or product level, and the technology level. It leverages real options analysis for managerial decision-making under uncertainty across these contexts. We also identify a set of real options—compatibility, sponsorship and ownership option—which are unique to these settings, and which provide a template for managerial thinking and analysis when it is possible to delay an investment decision. We employ a hybrid jump-diffusion process to model countervailing and complementary network effects from the perspective of a user or a firm joining a network. We also do this from the perspective of a network developer. Our analysis shows that when countervailing and complementary network effects occur in the same network technology context, they give rise to real option value effects that may be used to control or modify the valuation trajectory of a network technology. The option value of waiting in these contexts jumps when the related business environment experiences shocks. Further, we find that the functional relationship between network value and the option value is not linear, and that taking into account a risk premium may not always result in a risk-neural investment. We also provide a managerial decision-making template through the different kinds of deferral options that we identify for this IT analysis context.

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Notes

  1. A risk premium is an additional amount of payoff above the risk-free rate of interest to make a decision-maker indifferent between a higher risky payoff and a lower non-risky payoff [53]. Decision-makers who exhibit risk-neutral attitudes are indifferent to the risks involved and are only concerned about expected returns.

  2. Two events are independent if the occurrence of one of the events gives us no information about whether the other event will occur; that is, the events have no influence on each other. When two variables co-vary, change in one is accompanied by change in other, and they are said to be correlated. Although independence implies no correlation, lack of correlation does not imply independence. In real-world settings, dx may be related to Y.

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Acknowledgments

This article was first presented at the 20th Anniversary Symposium on Competitive Strategy, Economics and Information Systems at the 2007 Hawaii International Conference on Systems Science, in January 2007. The authors benefited from feedback from Michel Benaroch, Rajiv Dewan, Eric Clemons, and other participants. We are grateful to Indranil Bardhan, for his guidance in the development of this article for Information Technology and Management, and for the helpful suggestions of three anonymous reviewers. We also appreciated the interest of the special issue guest editors, Paul Tallon and Alok Gupta, in our work. We thank Qizhi Dai, Ryan Sougstad, and the participants of our doctoral seminars at Arizona State University and the University of Minnesota for discussions on related research problems at an early stage in the development of this research. Recent discussions with Murray Cantor and Clay Williams of IBM, and Scott Matthews of Boeing have also added value to this work. Rob Kauffman acknowledges support and funding from the MIS Research Center at the University of Minnesota and the Center for Advancing Business through Information Technology at Arizona State University, as well as the W. P. Carey Chair. Finally, Ajay Kumar is grateful for doctoral fellowship funding from the Graduate School of the University of Minnesota.

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Authors and Affiliations

  1. W. P. Carey Chair in Information Systems, Center for Advancing Business through Information Technology, W. P. Carey School of Business, Arizona State University, Tempe, AZ, 85287, USA

    Robert J. Kauffman

  2. Information Technology, Government of Kerala, Trivandrum, 695001, Kerala, India

    Ajay Kumar

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Correspondence to Robert J. Kauffman.

Appendix

Appendix

We now provide some additional details to further explain the modeling analysis that we conducted for the development of the results that are presented in this article.

1.1 Differential real option value

To obtain the result we have described, we analyzed the differential real option value for the network technology investment, which can be expressed as:

$$dROV = ROV_{t} dt + ROV_{R} dR^{{U'}} + ROV_{I} dI^{U} + (1/2)ROV_{{RR}} (dR^{{U'}} )^{2} + (1/2)ROV_{{II}} (dI^{U} )^{2} + (1/2)ROV_{R} ROV_{I} dR^{{U'}} dI^{U} + [ROV(YR^{U} ) - ROV(R^{U} )^{2} ]dq$$
(A1)

The superscripted notation denotes the partial differentials with respect to the variables, I U and R U, which represent investment I and the value of the revenues R that user U is able to obtain for its network technology investment. We are able to conclude that the real option value function ROV(R U, I U, t) is non-linear because the last term in Eq. A1 does not linearly relate to changes in differential real option value, dROV, with incremental changes dq in the variable q.

1.2 Application of the Bellman optimality equation

We used a risk-neutral process for the continuous part of the real option value function of the network, and substituted the equations for dR, dI U, ρ RI , dROV and dR U′ into the Bellman optimality equation, the r f ROVdt = E(dROV), the risk-free rate of interest r f . The Bellman optimality equation says that the value of a state under the optimal policy—in this case the value of the real option—must equal the expected return for the best action from that state [63]—in other words, the exercise of the real option. The Bellman equation has to satisfy two boundary conditions to be optimal. The value of the real option must be 0 at time T (the end of the horizon), because the decision to join the network cannot be deferred anymore, so that ROV(V U, I U, T) = 0. A second condition is that at any other time, 0 ≤ t < T, the value of the real option is always non-negative, and represents the value and the cost of joining the network for the user, so ROV(V U, I U, t) ≥ max[0, V U(t) − I U(t)].

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Kauffman, R.J., Kumar, A. Network effects and embedded options: decision-making under uncertainty for network technology investments. Inf Technol Manage 9, 149–168 (2008). https://doi.org/10.1007/s10799-008-0037-y

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