Data Portability on the Internet

An Economic Analysis

Abstract

Data portability allows users to transfer data between competing online services. As data gets increasingly valuable for online services and users alike, the enforcement of data portability within the European Union by the General Data Protection Regulation will have important ramifications for the competition in online markets. Thus, this paper develops a game-theoretic model to examine firms’ strategic reaction to data portability and to identify the ensuing market outcomes. It can be shown, among others, that although data portability is designed to protect users, they may be hurt because market entrants have an incentive to increase the amount of collected data compared to a regime without data portability. However, profits for new services and total surplus increase if the costs for implementation are not too large. This likely improves innovation and service variety. Consequently, the results provide important insights and case-specific recommendations for managers and policy makers in data-driven online markets.

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Notes

  1. 1.

    We do not consider consumption-related benefits for users, i.e., the base utility \(v_i\) for CP i does not depend on the amount of entered data, additionally, see Sect. 6.2.

  2. 2.

    As shown in “Appendix 4”, it is irrelevant whether we assume users to be myopic or strategic.

  3. 3.

    In “Appendix 5”, we show that the entrant CP B always requires at least the amount of data CP A required in \(t=1\) if \(v_B \ge v_A\). Users then only need to reveal the net amount of required data. If \(v_B\in [{15v_A}/{16}, v_A)\), CP B sets a lower data consumption level than CP A. Then users that switch CPs derive a net benefit from a right to data portability because (1) the new service requires less data and (2) the old service has to delete already entered data due to the right to erasure which is part of the GDPR (c.f., European Commission 2016b, Article 17 and “Appendix 5”).

  4. 4.

    Formally, the derivative changes its sign in the feasible parameter range. The effect of an increasing \(\tau\) on \(\pi _A^P\) is positive if \(\tau > {\sqrt{22v_A^2-12v_A v_B+4v_B^2}}/{6}\); the effect of an increasing \(\tau\) on \(\pi _A^{NP}\) is positive if \(\tau > {\sqrt{26v_A^2-12v_A v_B+4v_B^2}}/{6}\); the effect of an increasing \(\tau\) on \(\pi _B^{NP}\) is positive if \(\tau > {(6v_B-9v_A)}/{16}\).

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Acknowledgements

I wish to present my special thanks to Daniel Schnurr for valuable feedback, discussions, and proofreading. Moreover, I thank Jan Krämer, Oliver Zierke, participants of the International Conference on Information Systems (2017, Seoul, Republic of Korea), participants of the European Conference of the International Telecommunications Society (2017, Passau, Germany), as well as the entire reviewing team for their very valuable comments. The author acknowledges partial funding for this project from the Bavarian State Ministry of Science and the Arts in the framework of the Centre Digitisation.Bavaria. All remaining errors are my own.

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Correspondence to Michael Wohlfarth.

Additional information

This paper is an extended and revised version of Wohlfarth (2017).

Accepted after two revisions by Oliver Hinz.

Appendices

Appendix 1: Notation

The notation of the game-theoretic model outlined in Sect. 3 and solved in Sect. 4 is stated according to its occurrence in the text in Table 1. Moreover, the notation introduced in Sect. 5 is presented.

Table 1 Notation used in the game-theoretic model and its extension

Appendix 2: Thresholds for the Feasible Parameter Range

In this paper, we build on Hotelling’s model of horizontal differentiation (c.f., Hotelling 1929) in order to identify the competitive effects of introducing a right to data portability. In doing so, we assume that a unit mass of users is uniformly distributed on the interval [0, 1]. By calculating market shares, which can directly be deduced from the location of the indifferent user, we formally need to ensure that the indifferent user is in all cases located within the interval [0, 1]. Consequently, for the regime with data portability and for the regime without data portability, we require \(x^{*,d,1} \le 1, x^{*,d,2} \ge 0\) and \(x^{*,d,2} \le 1\), i.e., the CPs’ market shares are always positive and do not exceed 100%. As highlighted above, we assume (1) full market coverage in \(t=2\) for analytical tractability and (2) to analyze the effects of data portability, an entrant’s base utility that is large enough so that (at least) one user can potentially port its user data from CP A to CP B, i.e., \(U_B^{d,2}(x^{*,d,1}) \ge 0\). These assumptions lead to several conditions and thresholds stated next.

With a right to data portability. The following thresholds for \(\tau\) refer to the regime with a right to data portability.

  • Condition P1: Indifferent user in \(t=1\) within the feasible parameter range

    $$\tau > th\_p\_1 := \frac{v_A}{2}.$$
  • Condition P2: Indifferent user in \(t=2\) within the feasible parameter range (market share smaller 100%)

    $$\tau > th\_p\_2 := \frac{v_A-v_B}{3}.$$
  • Condition P3: Indifferent user in \(t=2\) within the feasible parameter range (market share larger 0%)

    $$\tau > th\_p\_3 := \frac{-v_A+v_B}{3}.$$

    Condition P4: Overlapping market shares (full market coverage), i.e., at least one user has to be able to port its data

    $$\tau < th\_p\_4 := \frac{5v_A}{12}+\frac{v_B}{3}.$$

Without a right to data portability. The following thresholds for \(\tau\) refer to the regime without a right to data portability.

  • Condition \(N\, P1\): Indifferent user in \(t=1\) within the feasible parameter range

    $$\tau > th\_np\_1 := \frac{7v_A+v_B}{20}.$$
  • Condition \(N\,P2\): Indifferent user in \(t=2\) within the feasible parameter range (market share smaller 100%)

    $$\tau > th\_np\_2 := \frac{9v_A-6v_B}{16}.$$
  • Condition \(N\,P3\): Indifferent user in \(t=2\) within the feasible parameter range (market share larger 0%)

    $$\tau > th\_np\_3 := \frac{v_B}{3}-\frac{v_A}{2}.$$
  • Condition \(N\,P4\): Overlapping market shares (full market coverage)

    $$\tau < th\_np\_4 := \frac{5v_A}{24}+\frac{v_B}{3}.$$

    Please note that these conditions restrict the feasible parameter range where the regime with and without data portability can be compared in. We account for these thresholds by comparing the regimes with and without data portability only in those cases where the value of \(\tau\) is feasible in both regimes. This “lowest common denominator” delimits the feasible parameter range used for the analyses, i.e., we require

    $$\tau \in [max\{th\_p\_1,th\_p\_2,th\_p\_3,th\_np\_1,th\_np\_2,th\_np\_3\}, \quad min\{th\_p\_4,th\_np\_4\}].$$

Appendix 3: Location of the Indifferent User

In the following, we show that \(U_A^{1}(x^{*,d,2}) \ge 0\) is satisfied in all relevant cases, i.e., the indifferent user in period two is given by \(x^{*,P,2} = - {(r_A^{2} + r_A^{1} - r^2_B - \tau - v_A + v_B)}/{2 \tau }\)with data portability, and by \(x^{*,NP,2} = - {(r_A^{2} - r^2_B - \tau - v_A + v_B)}/{2 \tau }\)without data portability.

In doing so, assume \(U_A^{1} (x^{*,d,2} ) < 0\). The location of the indifferent user is then calculated by solving \(v_A - \tau \cdot x - r_A^{2} - r_A^{1} = v_B - \tau \cdot (1-x) - r^2_B\) which yields \(x_{new}^{*,2} = x^{*,P,2} = - {(r_A^{2} + r_A^{1} - r^2_B - \tau - v_A + v_B)}/{2 \tau }\). Note that by assuming \(U_A^{1} (x^{*,d,2} ) < 0\), the indifferent user is located right to the indifferent user in period \(t=1\), i.e., \(x_{new}^{*,2} > x^{*,d,1}\). Consequently, users do not port their data although they would be able to do so, i.e., now the case with and without data portability coincides. We use \(x_{new}^{*,2}\) to specify firms’ profits. Again, we solve the game through backward induction. We use the obtained equilibrium results and calculate \(U_A^{1}(x_{new}^{*,2})\). The resulting term is only smaller than zero iff \(\tau > \tau ^{min} := {2v_A}{3} + {v_B}/{3}\). However, we assumed that CP B’s base utility is large enough so that at least one user can potentially port its user data (see above). This implies that \(\tau < \tau ^{max} = th\_p\_4 := {5v_A}{12} + {v_B}/{3}\). It can easily be seen that \(\tau ^{min} > \tau ^{max}\). Consequently, proofing by contradiction, \(U_A^{1} (x^{*,d,2} ) \ge 0\) is always satisfied.

Appendix 4: Myopic versus Strategic Users

In the following, we show that it is irrelevant whether users are assumed to be myopic or strategic. In doing so, first, consider the regime without a right to data portability. Here, the analysis remains identical due to the two stages assumed for our game-theoretic model and the assumption that data revealed in \(t=1\) does not lead to a disutility for users in \(t=2\). Thus, users do not have any benefit in \(t=2\) if they reveal more data in \(t=1\). Furthermore, CPs have no incentive to reduce their data consumption in case users provided additional data. Second, consider the regime with a right to data portability and assume a strategic user that is willing to accept a negative utility in \(t=1\) to be able to port (more) data to CP B in \(t=2\). However, CP B would then simply increase its data consumption in \(t=2\) leading to users being worse off compared to a user that is not willing to accept a negative utility in \(t=1\). Similar, also CP A has no incentive to reduce its data consumption as users do not experience a further disutility from data revealed in \(t=1\). Consequently, users would also suffer with data portability if they do not switch to CP B. Thus, in conclusion, users would unambiguously be worse off if they decide to accept a negative utility in \(t=1\) which is why they would not be willing to accept a negative utility in the first place. Consequently, assuming strategic users would not change the model’s results as users’ decisions coincide.

Appendix 5: Amount of Required Data \((r^t_i)\)

The equilibrium amount of required data is (c.f., Sect. 4.1):

$$\begin{aligned} r_A^{*,P,1}&= \frac{v_A}{2} \\ r_A^{*,P,2}&= \frac{6\tau -v_A-2v_B}{6} \\ r_B^{*,P,2}&= \tau -\frac{v_A-v_B}{3} \\ r_A^{*,NP,1}&= \frac{3\tau +10v_A-v_B}{17} \\ r_A^{*,NP,2}&= \frac{15\tau -v_A-5v_B}{17} \\ r_B^{*,NP,2}&= \frac{3\tau +10v_A-v_B}{17} \end{aligned}$$

The second order conditions are:

$$\begin{aligned} \frac{\partial ^2 \pi ^{P,1}_A}{\partial (r^1_A)^2 }&= - {2}/{\tau }< 0\\ \frac{\partial ^2 \pi ^{P,2}_A}{\partial (r^2_A)^2 }&= - {1}/{\tau }< 0\\ \frac{\partial ^2 \pi ^{P,2}_B}{\partial (r^2_B)^2 }&= - {1}/{\tau }< 0\\ \frac{\partial ^2 \pi ^{NP,1}_A}{\partial (r^1_A)^2 }&= - {17}/{9\tau }< 0\\ \frac{\partial ^2 \pi ^{NP,2}_A}{\partial (r^2_A)^2 }&= - {1}/{\tau }< 0\\ \frac{\partial ^2 \pi ^{NP,2}_B}{\partial (r^2_B)^2 }&= - {1}/{\tau } < 0\end{aligned}$$

Consequently, the equilibrium amount of required data for CP A and CP B, respectively, constitute the profit maximizing data consumption.

Moreover, it can easily be shown that the amount of data CP A requires is higher under a regime without data portability \((d=NP)\). For the first period, the amount of required data with data portability can only be higher if \(\tau < - {v_A}/{2}+ {v_B}/{3}\). In the second period, the amount of required data with data portability can only be higher if \(\tau > {11v_A}/{12}+ {v_B}/{3}\). However, both conditions violate the feasible parameter range defined in “Appendix 2”. Similar, \(r_B^{*,NP,2}\) can only be higher than \(r_B^{*,P,2}\) iff \(\tau > - {10v_A}/{3}+ {v_B}/{3}\). Again, this condition violates the feasible parameter range defined in “Appendix 2”. Consequently, within the feasible parameter range \(r_A^{*,NP,1}> r_A^{*,P,1}, r_A^{*,NP,2} > r_A^{*,P,2}\), and \(r_B^{*,NP,2} < r_B^{*,P,2}\).

Next, we like to highlight the different cases that may occur with regard to CP’s data consumption to provide further intuition for the utility functions stated in Sect. 3.

  • (case i) – users cannot port their data\((d=NP)\). The derived utility at CP B can be calculated the same way as the derived utility for users that decided to use CP A in \(t=1\). Depending on \(r^2_B\), more or less users are willing to switch to CP B. As we assume the market to be fully covered, users switch or become active at CP B if \(U^{NP,2}_B > U_A^{NP,2}\). Please note that in this case, users need to re-enter the already revealed data because they have no possibility to port their data. From an analytical perspective, it is not relevant whether CP B requires more or less data than CP A. The decision which CP to patronize is only affected by the resulting utility which – of course – is influenced by the amount of required data set by the respective CP. The indifferent user can be derived by solving \(v_B-\tau (1-x)-r^2_B=v_A-\tau x-r_A^2\) with respect to x (c.f., Sect. 4).

  • (case ii)–users can port their data\((d=P)\). The derived utility at CP B is now influenced by the amount of data CP A required from users in \(t=1\). Please note that due to the full market coverage assumption and in line with the assumptions highlighted in Sect. 3 as well as “Appendix 3”, users (again) switch or become active at CP B if \(U^{P,2}_B > U_A^{P,2}\). For users that have not been active at CP A in \(t=1\) (i.e., \(U_A^{1} < 0\)), the utility function for users deciding to use CP B equals the one from the no portability case (\(d=NP\), see above) because these users simply need to reveal all of the required data. For users that have been active at CP A in \(t=1\) and now switch to CP B, two sub-cases can be differentiated:

  • sub-case a) \(r^2_B \ge r_A^1\): Users have to reveal additional information if they become active at CP B. For example, users already revealed their name and address (\(r^1_A\)) but CP B requires their name, address and cellphone number (\(r^2_B\)). As users can port their data, they do not need to re-enter their name and address but need to (additionally) reveal their cellphone number which induces a disutility. This represents the most intuitive scenario. The resulting utility function for users that switch to CP B thus is \(v_B- \tau \cdot (1-x)-r^2_B+r_A^1\) and the indifferent user can be calculated by solving \(v_B- \tau \cdot (1-x)-r^2_B+r_A^1=v_A- \tau \cdot x -r_A^2\) with respect to x (c.f., Sect. 4).

  • sub-case b) \(r^2_B < r_A^1\): Users need to reveal less data at CP B. Analytically, this case only occurs iff \(v_B<v_A \wedge v_B >{15v_A}/{16}\), i.e., \(v_B\in [ {15v_A}/{16},v_A)\). In all other cases, either no feasible parameter range exists, or \(r^2_B \ge r_A^1\) (c.f., sub-case a). Consequently, in almost all cases considered in this paper, CP B requires at least the amount of data CP A required in period \(t=1\), which is why the examples and intuition provided focus on these cases. If CP B requires less data, users do not need to reveal additional data. Consequently, they do not experience a disutility if they switch to CP B in \(t=2\), i.e., all data required at CP B is ported. We assume that the resulting utility function for users that switch to CP B (again) is \(v_B- \tau \cdot (1-x)-r^2_B+r_A^1\) which is in line with the intuition of the disutility a user derives from revealing data being some kind of privacy costs (c.f., Sect. 1). Consequently, the user derives a net benefit from porting data because (1) the new service offered by CP B requires less data that does not need to be re-entered and (2) the data already provided to CP A is deleted at that CP because the European General Data Protection Regulation also encompasses a right to erasure (c.f., European Commission 2016b, Article 17), i.e., in the end, less data is disclosed to online services. The indifferent user can thus be calculated by solving \(v_B- \tau \cdot (1-x)-r^2_B+r_A^1=v_A- \tau \cdot x -r_A^2\) with respect to x (c.f., Sect. 4).

Appendix 6: CPs’ Profits \((\pi _i^d)\)

With data portability \((d=P)\), the CPs’ profits are:

$$\begin{aligned} \pi _A^P&= \frac{18\tau ^2+ 12 \tau (v_A-v_B) + 11 v_A^2 - 4 v_Av_B + 2v_B^2}{36 \tau }, \\ \pi _B^{P}&= \frac{(3\tau - v_A + v_B)^2}{18 \tau }. \end{aligned}$$

Without data portability \((d=NP)\), the CPs’ profits are:

$$\begin{aligned} \pi _A^{NP}&= \frac{18\tau ^2 + \tau (18v_A-12v_B) + 13v_A^2 - 6v_Av_B + 2v_B^2}{34 \tau }, \\ \pi _B^{NP}&= \frac{(16\tau - 9v_A + 6v_B)^2}{578 \tau }. \end{aligned}$$

To determine whether CPs are better off with data portability, we calculate the intersection of the CP’s profit functions under the different regimes (i.e., \(\pi _i^P\) and \(\pi _i^{NP}\)). Although the profit functions intersect two times, both intersections are outside the feasible parameter range given by the restrictions specified in the “Appendix 2”. Consequently, the effect of data portability on the incumbent and entrant is unambiguous. It can easily be shown that the incumbent (entrant) always suffers (benefits) from data portability, i.e., \(\pi _A^P \le \pi _A^{NP}\) and \(\pi _B^P \ge \pi _B^{NP}\).

Appendix 7: Consumer’s Surplus \((CS_i^d)\)

With data portability \((d=P)\), consumer’s surplus equals:

$$\begin{aligned} CS_A^P&= \frac{-45\tau ^2 + \tau (24v_A+30v_B) + 22v_A^2 - 8v_Av_B + 5v_B^2}{72 \tau }, \\ CS_B^{P}&= \frac{-45\tau ^2 + \tau (12v_A+6v_B) + 7v_A^2 - 4v_Av_B+ 7 v_B^2}{72 \tau }. \end{aligned}$$

Without data portability \((d=NP)\), consumer’s surplus equals:

$$\begin{aligned} CS_A^{NP}&= \frac{-1368\tau ^2 + \tau (264v_A+912v_B) + 763v_A^2 -88v_Av_B + 152v_B^2}{2312 \tau }, \\ CS_B^{NP}&= \frac{(16\tau -9v_A+6v_B )(80\tau -45v_A+38v_B)}{2312 \tau }.\end{aligned}$$

To determine whether users are better off with data portability, we calculate \(CS_A^P + CS_B^P = CS_A^{NP} + CS_B^{NP}\) and reorder the result with respect to \(\tau\). This leads to two solutions labeled by \(\tau _{CS}\) and \(\tau _{CS,2}\). It can be shown that \(\tau _{CS} := {(174v_B-822v_A+17\sqrt{6658v_A^2-752v_A v_B+16v_B^2})}/{726}\) can be within the feasible parameter range specified in “Appendix 2”, whereas \(\tau _{CS,2} := {(174v_B-822v_A-17\sqrt{6658v_A^2-752v_A v_B+16v_B^2})}/{726}\) is always outside of that feasible parameter range. Consequently, the effect of data portability on consumer’s surplus is ambiguous and users may suffer from a right to data portability. Whereas the effect of data portability on consumer’s surplus is positive if \(\tau < \tau _{CS}\), the effect is negative if \(\tau > \tau _{CS}\). Please note that \(\tau _{CS}\) is not always within the feasible parameter range: if \(v_B < {447 v_A}/{160}\), the intersection is always outside the feasible parameter range.

Appendix 8: Total Surplus \((TS^d)\)

With data portability \((d=P)\), total surplus is:

$$TS^P = \frac{-18 \tau ^2 + 36 \tau (v_A+v_B) + 55v_A^2 - 20v_Av_B + 10v_B^2}{72 \tau }.$$

Without data portability \((d=NP)\), total surplus is:

$$TS^{NP} = \frac{- 200 \tau ^2 + \tau (888v_A + 496v_B) + 783v_A^2 - 500v_Av_B + 178v_B^2}{1156 \tau }.$$

All intersections of the functions are outside the feasible parameter range specified by the restrictions given in “Appendix 2”. Consequently, the effect on total surplus is unambiguous. It can easily be shown that total surplus always increases with data portability, i.e., \(TS^P > TS^{NP}\). Please note that this result assumes that total surplus is the unweighted sum of producer’s and consumer’s surplus.

Appendix 9: Fixed Costs for Data Portability (F)

By introducing fixed costs F for implementing a right to data portability, CP A’s profits can be calculated by \(\pi _{A,F}^P=\pi _A^P - F\) and CP B’s profits by \(\pi _{B,F}^P=\pi _B^P - F\), respectively. Note that the profit functions without a right to data portability \((d=NP)\) remain unchanged because CPs do not face any additional costs if they do not have to implement such functionalities, i.e., \(\pi _{A,F}^{NP}=\pi _A^{NP}\) and \(\pi _{B,F}^{NP}=\pi _B^{NP}\).

We solve for the subgame perfect Nash equilibrium through backward induction. For the regime without a right to data portability, the results equal the results from the base scenario because \(\pi _{B,F}^{NP}=\pi _B^{NP}\) (c.f., Sect. 4.1 as well as “Appendix 6”). For the regime with a right to data portability incorporating costs for the implementation, we get

$$\begin{aligned} r_{A,B}^{*,P,1}&= \frac{v_A}{2}, \\ r_{A,B}^{*,P,2}&= \tau - \left( \frac{v_A+2v_B}{6}\right) , \\ r_{B,B}^{*,P,2}&= \frac{v_B-v_A}{3} + \tau . \end{aligned}$$

These results can be used to specify the CPs profits (c.f., Sect. 4.2).

Comparing the therewith deduced results, it can be seen that the entrant CP B now can be worse off with a right to data portability, if the fixed costs for the implementation exceed the critical threshold \(\hat{F}\). This threshold can be calculated by solving \(\pi ^{P}_{B,F} = \pi ^{NP}_{B,F}\) with respect to F, i.e., we solve

$$\begin{aligned} &\pi ^{P}_{B,F} = \pi ^{NP}_{B,F}, \\ &\frac{9\tau ^2 + (6v_B - 6v_A -18 F)\tau + (v_A-v_B)^2}{18 \tau } = \frac{(16\tau - 9v_A + 6v_B)^2}{578 \tau }.\end{aligned}$$

with respect to F which specifies the critical threshold \({\hat{F}}\). It follows that the entrant CP B is worse off, if

$$F > {\hat{F}} := \frac{(10v_A-v_B+3\tau )\cdot (35v_B-44v_A+99\tau )}{5205 \cdot \tau }.$$

Appendix 10: Porting Irrelevant Data (ID)

Assuming that users also port irrelevant data from CP A to CP B, a user’s utility function changes to \(U_{B,ID}^{d,2}(x)\) if they become active at CP B. Consequently, also the location of the indifferent user changes in period \(t=2\). Note that CP A’s utility function and the location of the indifferent user in \(t=1\) remains unchanged.

To calculate the indifferent user in \(t=2\), we (again) need to account for the different cases that may evolve. We stick to the assumption used in the base model. Thus, if users have the possibility to port their data (\(d=P\) with subscript ID), the indifferent user in \(t=2\) can be calculated by solving \(v_A - \tau \cdot x - r_A^{2} = v_B - \tau \cdot (1-x) - r^2_B + \gamma \cdot r_A^{1}\). The indifferent user without data portability \((d=NP)\) can (again) be calculated by solving \(v_A - \tau \cdot x - r_A^{2} = v_B - \tau \cdot (1-x) - r^2_B + r_A^{1}\). Consequently, the indifferent user in \(t=2\) is located at

$$x_{ID}^{*,d,2}= {\left\{ \begin{array}{ll} - \frac{r_A^{2}+ \gamma \cdot r_A^{1}-r^2_B-\tau -v_A+v_B}{2\tau } &{} \text {, if } U_A^{1}(x_{ID}^{*,d,2})\ge 0, d=P \\ - \frac{r_A^{2}-r_B-\tau -v_A+v_B}{2\tau } &{} \text {, else (} U_A^{1}(x_{ID}^{*,d,2})\ge 0; d=NP). \end{array}\right. }$$

Based on the market shares given by the location of the indifferent user, the profits of the CPs can be specified. The total profits of CP A for both periods are given by

$$\pi _{A,ID}^d = \underbrace{x^{*,d,1} \cdot r_{A,ID}^{d,1}}_{\pi _{A,ID}^{d,1}} + \underbrace{x_{ID}^{*,d,2} \cdot (r_{A,ID}^{d,1} + r_{A,ID}^{d,2})}_{\pi _{A,ID}^{d,2}}$$

CP B, which is only active in \(t=2\), makes total profits of:

$$\begin{aligned} \pi _{B,ID}^d&= (1-x^{*,d,1}) \cdot r^{d,2}_{B,ID} + (x^{*,d,1} - x_{ID}^{*,d,2}) \cdot ((r_{B,ID}^{d,2} - \gamma \cdot r_{A,ID}^{d,1}) + \gamma \cdot r_{A,ID}^{d,1}), \\ \pi _{B,ID}^d&= (1-x_{ID}^{*,d,2})\cdot r_{B,ID}^{d,2}. \end{aligned}$$

Using the equilibrium amounts of required data stated above, we receive:

$$\begin{aligned} \pi _{A,ID}^P&= \frac{(2\gamma - 13) v_A^2+6v_A \left( \tau - {v_B}/{3}\right) (\gamma -3) -18 \left( \tau - {v_B}/{3}\right) ^2}{2\tau (\gamma ^2 - 2\gamma -17)}, \\ \pi _{B,ID}^P&= \frac{2 \left( \gamma ^2 \tau - \gamma \left( 2\tau + {3v_A}/{2}\right) - 8 \tau + {9v_A}/{2} - 3v_B \right) ^2}{\tau (\gamma ^2 - 2\gamma -17)^2}, \\ \pi _{A,ID}^{NP}&= \pi _{A}^{NP}, \\ \pi _{B,ID}^{NP}&= \pi _{B}^{NP}.\end{aligned}$$

For consumer’s surplus, we receive:

$$\begin{aligned} CS_{A,ID}^P&= \frac{1}{8\left( \left( \gamma ^2-2\gamma -17\right) ^2\tau \right) }\cdot \left( 4\gamma ^4 v_A^2 -\left( 24\left( \tau + {v_A}/{2}- {v_B}/{3}\right) \right) v_A \gamma ^3 \right. \\ &\quad \left. + \left( -113v_A^2+(60\tau -20v_B)v_A \right. \right. \\ &\quad \left. \left. +36\left( \tau - {v_B}/{3}\right) ^2\right) *\gamma ^2+ \left( 150v_A^2 + \left( 564\tau -188v_B\right) v_A - 288\left( \tau - {v_B}/{3}\right) ^2 \gamma \right) \right. \\ &\quad \left. + 763v_A^2+(264\tau -88v_B)v_A - 1368\left( \tau - {v_B}/{3}\right) ^2\right) ,\\ CS_{B,ID}^P&= \frac{1}{8\left( \left( \gamma ^2-2\gamma -17\right) ^ 2\tau \right) }\cdot ((-20\tau ^2+(24v_A+8v_B)\tau +8v_A(v_A-v_B))\gamma ^4\\ &\quad +(8\tau ^2+(-96v_A+16v_B)\tau \\ &\quad -116v_A^2+40v_Av_B-8v_B^2)\gamma ^3 +(600\tau ^2+(84v_A-288v_B)\tau +295v_A^2\\ &\quad -68v_Av_B+16v_B^2)\gamma ^2 \\ &\quad + (-928\tau ^2 +(-1020v_A+352v_B)\tau +470v_A^2+252v_Av_B+16v_B^2)\gamma \\ &\quad -\left( 1280\left( \tau + {(6v_B-9v_A)}/{16}\right) \cdot \left( - {9v_A}/{16}- {19v_B}/{40}+\tau \right) \right) , \\ CS_{A,ID}^{NP}&= CS_{A}^{NP}, \\ CS_{B,ID}^{NP}&= CS_{B}^{NP}.\end{aligned}$$

Users can be worse off with a right to data portability if \(CS^P_{A+B,ID} < CS^{NP}_{A+B,ID}\). This occurs if

$$\begin{aligned} \tau > \tau _{CS,ID}:&= \frac{1}{522\gamma ^3+1380\gamma ^2-17394\gamma +28560} \\ &\quad \cdot (17\sqrt{1594} \left( \left( \left( \gamma ^2- {4430\gamma }/{767} + {6962}/{797}\right) v_A^2 \right. \right. \\ &\quad \left. \left. - {164v_Bv_A}/{797} \left( \gamma ^2- {183\gamma }/{41}+ {231}/{41}\right) + {8v_B^2}/{797}(\gamma -2)^2*(1/797)\right) \left( \gamma ^2\right. \right. \\ &\quad \left. \left. -2\gamma -17\right) ^{1/2}\right. \\ &\quad \left. +(436 v_A+106 v_B) \gamma ^3+(-2322 v_A+732 v_B) \gamma ^2+(7728 v_A\right. \\ &\quad \left. -4914 v_B) \gamma -20638 v_A+7208 v_B\right) .\end{aligned}$$

Restricting the amount of data that can be ported dampens the effect of data portability on consumer’s surplus. This may lead to users suffering less if the user’s mismatch costs are low. However, restricting the amount of data that can be ported also dampens the effect of data portability on consumer’s surplus if users benefit with a right to data portability. Consequently, compared to a scenario with full data portability (\(\gamma =1\)), consumer’s surplus with \(\gamma \in (0,1)\) is lower, i.e., \(CS^P_{A+B,ID} < CS^P_{A+B}\), if

$$\begin{aligned} \tau < \tau _{ID,P}:&= \frac{1}{30\gamma ^3+126\gamma ^2-882\gamma +726} \cdot (-\sqrt{1690} ( (\gamma ^2-2\gamma -17)^2 \left( \left( \gamma ^2\right. \right. \\ &\quad \left. - {3526\gamma }/{845}+ {3329}/ {845}\right) v_A^2 \\ &\quad \left. - {1}/{169}(32(\gamma -1) \left( \gamma - {47}/{20}\right) v_Bv_A) + {1}/{845} (8v_B^2(\gamma -1)^2) \right) ^{1/2} \\ &\quad +(30v_A+6v_B)\gamma ^3+(-126v_A+54v_B)\gamma ^2+(270v_A-234v_B)\gamma \\ &\quad -822v_A+174v_B).\end{aligned}$$

Total surplus can be calculated according to the formula given in Sect. 4.4.

Appendix 11: Diminishing Value of Collected Data (DV)

Assuming that the data collected in \(t=1\) is not equally important in period \(t=2\) does not change the user’s utility function or the entrant’s profit function. However, the incumbent CP A’s profit function changes as highlighted in Extension 5.3. This leads to a new equilibrium data consumption and subsequently, to diverting profits, consumer surplus, and total profits.

Using the equilibrium amounts of required data stated in Extension 5.3, we receive:

$$\begin{aligned}\pi _{A,DV}^P&= \frac{(-2\rho -9)v_A^2-(6(\rho +1))(\tau -(1/3)v_B)v_A-18(\tau -(1/3)v_B)^2}{2(\rho ^2-2\rho -17))\tau }, \\ \pi _{B,DV}^P&= \frac{2(\tau \rho ^2+(-2\tau +3v_A(1/2))\rho -8\tau +3v_A(1/2)-3v_B)^2}{2(\rho ^2-2\rho -17))\tau }, \\ \\ \pi _{A,DV}^{NP}&= \frac{(-2\rho -11)v_A^2-(6(\tau -(1/3)v_B))(\rho +2)v_A-18(\tau -(1/3)v_B)^2}{2(\rho ^2-18)^2\tau }, \\ \pi _{B,DV}^{NP}&= -\frac{(2\tau \rho ^2+3v_A\rho -18\tau +6v_A-6v_B)^2}{2(\rho ^2-18)^2\tau }.\end{aligned}$$

For consumer’s surplus, we receive:

$$\begin{aligned} CS_{A,DV}^P&= \frac{1}{8(\rho ^2-2\rho -17)^2\tau } \cdot (4v_A^2\rho ^4+60v_A(\tau -2v_A(1/15)-(1/3)v_B)\rho ^3 \\ &\quad +(7v_A^2+(-48\tau +16v_B)v_A+252(\tau -(1/3)v_B)^2)\rho ^2\\ &\quad +(306v_A^2+(-48\tau +16v_B)v_A\\ &\quad -288(\tau -(1/3)v_B)^2)\rho +483v_A^2+(900\tau -300v_B)v_A\\ &\quad -1584(\tau -(1/3)v_B)^2),\\ CS_{B,DV}^P&= \frac{1}{8(\rho ^2-2\rho -17)^2\tau } \cdot ((-20\tau ^2+8\tau v_B)\rho ^4+(80\tau ^2+(-84v_A-32v_B)\tau \\ &\quad -8v_A^2+20v_Bv_A)\rho ^3 \\ &\quad +(168 \tau ^2+48 v_A \tau -113 v_A^2\\ &\quad -8 v_A v_B-32 v_B^2) \rho ^2+(-712 \tau ^2\\ &\quad +(552 v_A+208 v_B) \tau \\ &\quad -62 v_A^2-32 v_A v_B+40 v_B^2) \rho -1136\tau ^2+(-84v_A+32v_B)\tau \\ &\quad +435v_A^2+164v_Bv_A+244v_B^2),\\ \\ CS_{A,DV}^{NP}&= \frac{1}{8(\rho ^2-18)^2\tau } \cdot (4v_A^2\rho ^4+60v_A(\tau +2v_A(1/15)-(1/3)v_B)\rho ^3 \\ &\quad (-5v_A^2+(96\tau -32v_B)v_A+252(\tau -(1/3)v_B)^2)\rho ^2\\ &\quad -(108(\tau -5v_A(1/3)-(1/3)v_B))v_A \rho \\ &\quad -(1620(-2v_A(1/3)-(1/3)v_B+\tau ))(8v_A(1/15)-(1/3)v_B+\tau )),\\ CS_{B,DV}^{NP}&= - \frac{1}{2(\rho ^2-18)^2\tau } \cdot (5(\tau \rho ^2-9\tau +(3/2)v_A \rho +3v_A-3v_B) \\ &\quad \cdot (\tau -2v_B(1/5))\rho ^2+3v_A\rho (1/2)-9\tau +3v_A+21v_B(1/5)). \end{aligned}$$

Users can be worse off with a right to data portability if \(CS^P_{A+B,DV} < CS^{NP}_{A+B,DV}\). This occurs if

$$\begin{aligned} \tau > \tau _{CS,DV}:&= \frac{1}{12\rho ^4+36\rho ^3-234\rho ^2-1080\rho +540} \cdot \left( 2 \left( \left( \left( \rho ^6-2\rho ^5-39\rho ^4\right. \right. \right. \right. \\ &\quad \left. \left. \left. \left. -34\rho ^3+741\rho ^2+1520\rho - {1045}/{2}\right) v_A^2\right. \right. \right. \\ &\quad \left. \left. \left. +4v_B\left( \rho 4-5\rho ^3- {41}/{2}\rho ^2- {95}/{2} \rho +25\right) v_A\right. \right. \right. \\ &\quad \left. \left. \left. +16v_B^2\left( \rho - {1}/{2}\right) ^2\right) (\rho ^2-18)^2\right) ^{1/2}-2v_A\rho ^5\right. \\ &\quad \left. +(-2v_A+4v_B)\rho ^4+(3v_A+4v_B)\rho ^3+(74v_A-74v_B)\rho ^2\right. \\ &\quad \left. +(180v_A-216v_B)\rho +540v_A+108v_B\right) ). \end{aligned}$$

Total surplus can be calculated according to the formula given in Sect. 4.4.

Appendix 12: Network Effects (NWE)

The Amount of Required Data

As highlighted in Sect. 5.4, with network effects, a user’s utility function changes. Because the location of the indifferent user changes, the corresponding profits change yielding different equilibrium amounts of required data. For CP A, the equilibrium amount of required data in \(t=1\) equals:

$$\begin{aligned}r_{A,NWE}^{*,P,1}&= r_{A}^{*,P,1} = \frac{v_A}{2},\\ r_{A,NWE}^{*,NP,1}&= r_{A}^{*,NP,1} - \frac{3 \omega }{17} = \frac{3 \tau + 10v_A -v_B-3\omega }{17}. \end{aligned}$$

and in \(t=2\):

$$\begin{aligned} r_{A,NWE}^{*,P,2}&= \tau - \omega - \frac{v_A}{6}- \frac{v_B}{3},\\ r_{A,NWE}^{*,NP,2}&= \frac{15(\tau -\omega ) -v_A - 5v_B}{17}.\end{aligned}$$

For CP B, the equilibrium amount of required data (in \(t=2\)) equals:

$$\begin{aligned} r_{B,NWE}^{*,P,2}&= r_{B}^{*,P,2}-\omega = \tau -\omega -\frac{v_A-v_B}{3},\\ r_{B,NWE}^{*,NP,2}&= r_{B}^{*,NP,2}-\frac{16\omega }{17} = \frac{16\tau -9v_A+6v_B-16\omega }{17}.\end{aligned}$$

CPs’ Profits

The calculation of the CPs’ profits incorporating network effects qualitatively remains unchanged compared to the base model (c.f., Sect. 3 for details). Using the location of the indifferent users (c.f., Extension 5.4) and the equilibrium amount of required data (c.f., Sect. 18.1), the CPs’ profits with data portability \((d=P)\) and with network effects yield:

$$\begin{aligned} \pi _{A,NWE}^P&= \frac{v_A^2}{4(\tau -\omega )} + \frac{(3(\tau -\omega )+v_A-v_B)^2}{18(\tau - \omega )},\\ \pi _{B,NWE}^P&= \frac{(3(\tau -\omega )-v_A+v_B)^2}{18\tau -18\omega }.\end{aligned}$$

Without data portability \((d=NP)\) and with network effects:

$$\begin{aligned} \pi _{A,NWE}^{NP} & = \frac{18(\omega ^2 + \tau ^2) +(-36\tau -18v_A+12v_B)\omega +12\tau (18v_A-12v_B)+13v_A^2-6v_Av_B+2v_B^2}{34 \tau - 34 \omega }, \\ &\pi _{B,NWE}^{NP} = \frac{(16(\tau -\omega )-9v_A+6v_B)^2}{578\tau -578\omega }. \end{aligned}$$

Consumer’s Surplus

For consumer’s surplus, we get:

$$\begin{aligned} CS_{A,NWE}^P&= \frac{1}{72(\tau -\omega )^2} \cdot (54\omega ^3+(-153\tau +18v_A+36v_B)\omega ^2 \\ &\quad + (144\tau ^2+(-42v_A-66v_B)\tau \\ &\quad -12v_A^2+6v_Av_B+6v_B^2)\omega -45\tau ^3+(24v_A+30v_B)\tau ^2\\ &\quad +(22v_A^2-8v_Av_B-5v_B^2)\tau ), \\ CS_{B,NWE}^P&= \frac{1}{72(\tau -\omega )^2} \cdot (-45\tau ^3+(12v_A+6v_B+144\omega )\tau ^2\\ &\quad +(-153\omega ^2+(-30v_A-6v_B)\omega \\ &\quad +7v_A^2+4v_Av_B+7v_B^2)\tau -6\omega (-9\omega ^2-3\omega v_A+v_A^2+v_Av_B+v_B^2)), \\ CS_{A,NWE}^{NP}&= \frac{1}{2313(\tau -\omega )^2} \cdot (1728\omega ^3+(-4824\tau +108v_A+1152v_B)\omega ^2\\ &\quad +(4464\tau ^2 +(-372v_A-2064v_B)\tau \\ &\quad -486v_A^2+36v_Av_B+192v_B^2)\omega -1368\tau ^3+(264v_A+912v_B) \tau ^2\\ &\quad +(763v_A^2-88v_Av_B-152v_B^2)\tau ,\\ CS_{B,NWE}^{NP}&= -\frac{160}{289(\tau -\omega )^2} \cdot \left( {6\omega ^2}/{5}+\left( - {11\tau }/{5} + {27v_A}/{40} + {2v_B}/{5}\right) \omega \right. \\ &\quad \left. +\tau \left( \tau - {9v_A}/{16} - {19v_B}/{40}\right) \right) \\ &\quad \cdot \left( - {9v_A}/{16}+ {3v_B}/{8}-\omega +\tau \right) . \end{aligned}$$

Users are worse off with a right to data portability if \(CS_{A,P}+CS_{B,P}<CS_{A,NP}+CS_{B,NP}\). The resulting threshold can be calculated by solving \(CS_{A,P}+CS_{B,P} = CS_{A,NP}+CS_{B,NP}\) with respect to \(\tau\). This yields \(\tau _{CS,NWE}\).

Total Surplus

Total surplus can be calculated according to the formula given in Sect. 4.4.

Comparison to the Base Model

Compared to the base model without considering network effects, the incumbent can benefit in terms of profits from the existence of network effects due to a higher market share in the first period. Analytically, the incumbent’s profit functions with and without the existence of network effects intersect within the feasible parameter range. If the user’s mismatch costs are high, the incumbent realizes higher profits with network effects. Formally, if \(\tau > {\omega }/{2} + {\sqrt{9\omega ^2+22v_A^2-8v_A v_B+4v_B^2}}/{6}\) (with data portability) and if \(\tau > {\omega }/{2} + {\sqrt{9\omega ^2+26v_A^2-12v_A v_B+4v_B^2}}/{6}\) (without data portability), the incumbent realizes higher profits if network effects are considered. Conversely, the entrant always realizes lower profits. Unsurprisingly, consumers are unambiguously better off if positive direct network effects are considered.

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Wohlfarth, M. Data Portability on the Internet. Bus Inf Syst Eng 61, 551–574 (2019). https://doi.org/10.1007/s12599-019-00580-9

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Keywords

  • Data portability
  • Competition between online services
  • Economics of IS
  • Switching costs
  • Market entry and innovation