1 Introduction
2 Network effects in two-sided markets
2.1 Previous research
Authors | Main research topics | Data gen. | Analysis methods | Industry/data sets | Economic dependent variables | Considers | |
---|---|---|---|---|---|---|---|
CNE | SNE | ||||||
Ackerberg and Gowrisankaran (2006) | NEs for banks and customers | T | Max. likelihood | ACH banking | Number of transactions | Yes | No |
Brynjolfsson and Kemerer (1996) | User base on price | M | Semi-log, OLS | Spreadsheet software | Prices | Yes | No |
Chacko and Mitchell (1998) | User base on company growth | M | OLS | 3 technology sectors | Corporate growth rate | Yes | No |
Chao and Derdenger (2013) | NEs on revenue-opt. price structure | M | Regression with IV | Portable game consoles | Associated prices | Yes | No |
Chen and Xie (2007) | Implications of customer loyalty | M | Regression | Newspaper | Advertising rate, market share diff. | Yes | No |
Chu and Manchanda (2013) | User base on other group’s growth | T | Max. likelihood | C2C retail platform | Growth of other user group | Yes | No |
Clements and Ohashi (2005) | Indirect NEs, hardw. diffusion | M | Two-stage least squares | Video game systems | Hardware and software adoption | Yes | No |
Gandal et al. (2000) | Hardw. prices and softw. on diffusion | M | OLS | CD players and titles | Change in variety and sales | Yes | No |
Mantrala et al. (2007) | Marketing invest on profits | M | Two-segment SURE | Newspapers | Subscriptions, ad revenue, sales | Yes | No |
Nair et al. (2004) | Indirect NEs in competition | M | Monte Carlo, OLS | PDAs and software | Hardw. demand, softw. provision | Yes | No |
Rysman (2004) | Importance of CNEs | M | Nested logit | Yellow pages | Consumer and advertiser demand | Yes | No |
Rysman (2007) | Card usage and acceptance | M, T | Logit | Payment card transactions | Choice of favorite network | Yes | No |
Shankar and Bayus (2003) | Network strength in competition | M | SEM | Video game consoles | Network strength | Yes | No |
Wilbur (2008) | Ads on audience size and vice versa | M | Logit | TV ads | Viewer and advertiser demand | Yes | No |
Asvanund et al. (2004) | Incremental value of new users | T | Logit, OLS | Peer-to-peer networks | Network value | Yes | Yes |
Sridhar et al. (2011) | Optimal marketing invests with CNEs | M | DMR | Local newspaper | Demand from both sides | Yes | (Yes) |
Tucker and Zhang (2010) | Installed base on listing behavior | F | Probit | Classifieds platform | Number of listings | Yes | Yes |
This paper | Network effects on revenue; revenue-optimal user split | T | SURE, logit, OLS | Online dating platform | Revenue, user net gain, number of subscribers | Yes | Yes |
2.2 Expected network effects on an online dating platform
2.2.1 Online dating
2.2.2 CNEs
2.2.3 SNEs
3 Theoretical validation: identifying direction and magnitude of network effects
3.1 Platform and data description
Number of registrations | Median user lifetime in days | Revenue share | |||||
---|---|---|---|---|---|---|---|
Women | Men | Total | Women | Men | Total | Women | Men |
3640 | 5283 | 8923 | 75 | 102 | 86 | 10.7 % | 89.3 % |
Min. | Max. | Mean | Median | SD | |
---|---|---|---|---|---|
Installed user base | 1365 | 1924 | 1536.7 | 1505 | 133.0 |
Number of new registrations | 1 | 22 | 7.38 | 7 | 3.61 |
Share of paying users in % | 3.74 | 7.71 | 6.21 | 6.37 | 0.92 |
Share of women in % | 35.5 | 41.1 | 38.4 | 38.3 | 1.1 |
User age (upon registration) in years | 18 | 99 | 37.1 | 35 | 11.3 |
Lifetime (of the platform) in days | 3835 | 4749 | 4292 | 4292 | 264.3 |
Silver customers | Gold customers |
P value (t test) | |
---|---|---|---|
No. of subscriptions | 595 | 41 | – |
Revenue per day
| |||
Average | €1.07 | €2.06 | 0.003 |
Median | €0.98 | €1.31 | |
SD | €0.98 | €4.01 | |
Subscription length in days
| |||
Average | 165 | 160 | 0.886 |
Median | 93 | 152 | |
SD | 214.9 | 132.8 | |
Total revenue per subscription
| |||
Average | €133.95 | €204.26 | 0.000 |
Median | €89.70 | €199.26 | |
SD | €147.34 | €156.57 |
3.2 Model and variables
3.2.1 Dependent variables
3.2.2 Independent variables
Covariate | Description | Min | Max | Median | SD |
---|---|---|---|---|---|
Women
| Installed base of female users on the previous day | 506 | 782 | 572 | 63.3 |
Men
| Installed base of male users on the previous day | 832 | 1144 | 931 | 73.1 |
PlatformLifetime
| Lifetime of the platform since launch (in days) | 3835 | 4749 | 4292 | 264.3 |
Update1
| Bug fixes, selected inactive users deleted | 0 | 1 | 1 | 0.34 |
Update2
| Payment website update | 0 | 1 | 1 | 0.45 |
Update3
| New payment website | 0 | 1 | 1 | 0.49 |
Update4
| Introduction of new flirt game (1) | 0 | 1 | 1 | 0.50 |
Update5
| New registration process | 0 | 1 | 0 | 0.48 |
Update6
| Introduction of monthly billing (step 1) | 0 | 1 | 0 | 0.46 |
Update7
| Introduction of monthly billing (step 2) | 0 | 1 | 0 | 0.43 |
Update8
| New Internet law implemented for payment website | 0 | 1 | 0 | 0.37 |
Update9
| Monthly billing complete | 0 | 1 | 0 | 0.37 |
Update10
| Introduction of new flirt game (2) | 0 | 1 | 0 | 0.11 |
TVevent1
| UEFA EURO 2010 | 0 | 1 | 0 | 0.11 |
TVevent2
| FIFA World Cup 2012 | 0 | 1 | 0 | 0.16 |
Winter
| Season | 0 | 1 | 0 | 0.41 |
Spring
| Season | 0 | 1 | 0 | 0.40 |
Summer
| Season | 0 | 1 | 0 | 0.46 |
Fall
| Season | (Omitted because of collinearity) |
3.3 Identification of CNEs and SNEs
Independent variables | Dependent variable: DailyRevenuePerWoman
| Dependent variable: DailyRevenuePerMan
| ||||||
---|---|---|---|---|---|---|---|---|
Model 1 | Model 2 | Model 3 | Model 4 | Model 1 | Model 2 | Model 3 | Model 4 | |
Installed base | ||||||||
Women
| −0.00233*** | −0.00327*** | −0.00324*** | −0.00495*** | 0.01414*** | 0.00798*** | 0.00664*** | |
Men
| 0.00099*** | 0.00203*** | 0.00274*** | −0.00819*** | −0.01917*** | −0.00772*** | −0.00831*** | |
Platform parameters | ||||||||
PlatformLifetime
| −0.00161*** | −0.00172*** | −0.00158*** | −0.00177*** | ||||
Update1
| 0.24203*** | 0.13408 | 1.92923*** | 1.177824*** | ||||
Update2
| 0.62657*** | 0.6469*** | 0.03142 | −0.09009 | ||||
Update3
| 0.2999*** | 0.24713*** | 0.41002*** | 0.12,682 | ||||
Update4
| −0.20911*** | −0.16,894*** | 0.21692** | 0.56356*** | ||||
Update5
| 0.18542*** | 0.18566*** | −0.87221*** | −0.85609*** | ||||
Update6
| −0.55129*** | −.58451*** | −0.32383*** | −0.3563*** | ||||
Update7
| 0.57989*** | 0.55077*** | 0.95582*** | 0.83301*** | ||||
Update8
| 0.08138*** | 0.10276*** | 0.36529*** | 0.24856*** | ||||
Update9
| 0.60853*** | 0.62466*** | −0.83949*** | −0.54311*** | ||||
Update10
| 0.27583*** | 0.32232*** | 0.5254*** | 0.58091*** | ||||
Seasonal parameters | ||||||||
TVevent1
| −0.5141*** | −1.17277*** | ||||||
TVevent2
| 0.11135** | 0.02654 | ||||||
Winter
| −0.08727** | 0.05107 | ||||||
Spring
| −0.07847* | 0.07906 | ||||||
Summer
| −0.02351* | 0.41086*** | ||||||
Constant | 2.77099*** | 2.23918*** | 7.3951*** | 8.34538*** | 14.97672*** | 16.99564*** | 14.79339*** | 17.02908*** |
Number of observations (days) | 914 | 914 | 914 | 914 | 914 | 914 | 914 | 914 |
R
2
| 0.1199 | 0.1259 | 0.5316 | 0.5485 | 0.3664 | 0.5229 | 0.7018 | 0.7444 |
Independent variables | Dependent variable: NetGainWomen
| Dependent variable: NetGainMen
| ||||||
---|---|---|---|---|---|---|---|---|
Model 1 | Model 2 | Model 3 | Model 4 | Model 1 | Model 2 | Model 3 | Model 4 | |
Installed base | ||||||||
Women
| −0.0052943* | −0.0187988** | −0.0647049** | −0.063719** | −0.0106566 | −0.0410637 | −0.022364 | |
Men
| 0.0130922** | −0.0237064 | −0.0366864 | −0.0074022* | 0.0030014 | −0.0538267** | −0.0760516** | |
Platform parameters | ||||||||
PlatformLifetime
| −0.0016744 | −0.0137804** | 0.0055423 | −0.0073152 | ||||
Update1
| −14.54164* | −16.75659* | −16.51846*** | −17.78324* | ||||
Update2
| 0.2594894 | 3.189207 | −1.454399 | 2.120249 | ||||
Update3
| −2.506983 | −1.784541 | −3.559547* | −2.754921* | ||||
Update4
| −0.4020995 | −0.5808471 | −1.340044 | −1.788673 | ||||
Update5
| 0.2353828 | 1.926006 | 1.081561 | 3.278738** | ||||
Update6
| −1.83712** | 0.2069084 | −0.9842817 | 2.111515* | ||||
Update7
| 4.191521*** | 4.927273*** | 3.126861* | 3.290054 | ||||
Update8
| 1.401801 | 2.04894 | −1.848275 | −1.146902 | ||||
Update9
| −1.101929 | −.6813836 | 0.7950864 | 1.252844 | ||||
Update10
| −1.498372 | −2.560496 | −0.5833106 | −2.264057 | ||||
Seasonal parameters | ||||||||
TVevent1
| −5.24849 | −0.0268828 | ||||||
TVevent2
| 0.5644956 | 1.164045 | ||||||
Winter
| 1.771118* | 2.985986*** | ||||||
Spring
| −0.6904099 | −0.5966981 | ||||||
Summer
| −0.3859537 | −0.001084 | ||||||
Constant | 3.017029* | −1.380181 | 81.15897** | 142.6788* | 6.891396* | 68.70649* | 129.7221* | |
Number of observations | 914 | 914 | 914 | 914 | 914 | 914 | 914 | 914 |
R
2
| 0.0003 | 0.0070 | 0.0932 | 0.1046 | 0.0001 | 0.0050 | 0.0898 | 0.1037 |
Independent variables | Dependent variable: NetGainWomen
| Dependent variable: NetGainMen
| ||||
---|---|---|---|---|---|---|
Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | |
Installed base (total) | ||||||
Users
| −0.0016396 | −0.0443007*** | −0.0497915* | −0.0033078 | −0.0474156*** | −0.0500245* |
Platform parameters | ||||||
PlatformLifetime
| −0.0020917 | −0.0148538** | 0.0056722 | −0.0051835 | ||
Update1
| −15.03112*** | −16.96543* | −16.36608*** | −17.36849* | ||
Update2
| 0.2033772 | 3.326949* | −1.436931*** | 1.846689 | ||
Update3
| −2.532174** | −1.657824 | −3.551705*** | −3.006583* | ||
Update4
| −1.004848 | −0.894958 | −1.152406 | −1.164841 | ||
Update5
| 1.528642 | 2.69635* | 0.6789633 | 1.748814 | ||
Update6
| −1.40788 | 0.6638192 | −1.117906 | 1.204078 | ||
Update7
| 4.228326*** | 5.070342*** | 3.115403** | 3.005915 | ||
Update8
| 1.447247 | 2.048838 | −1.862423 | −1.146699 | ||
Update9
| −1.505206 | −0.7951453 | 0.9206287 | 1.478778 | ||
Update10
| −1.061267 | −2.555395 | −0.7193835 | −2.274187 | ||
Seasonal parameters | ||||||
TVevent1
| −4.914585 | −0.6900263 | ||||
TVevent2
| 0.3246244 | 1.640435 | ||||
Winter
| 2.176263** | 2.181358** | ||||
Spring
| −0.5037326 | −0.9674439 | ||||
Summer
| −0.2441007 | −0.2828075 | ||||
Constant | 2.406945 | 90.62937*** | 151.0396** | 4.975004 | 65.75831** | 113.1174 |
Number of observations | 914 | 914 | 914 | 914 | 914 | 914 |
R
2
| 0.0012 | 0.0899 | 0.1035 | 0.0041 | 0.0896 | 0.1002 |
Independent variables | Dependent variable: DailyRevenueAllWomen
| Dependent variable: DailyRevenueAllMen
| Dependent variable: DailyRevenueAllUsers
| ||||||
---|---|---|---|---|---|---|---|---|---|
Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | |
Installed base | |||||||||
Women
| −0.0094565*** | −0.0121272*** | −0.0207466*** | 0.1214191*** | 0.0768262*** | 0.0687561*** | 0.1119683*** | 0.0647126*** | 0.0480195** |
Men
| 0.006163*** | 0.0132575*** | 0.0160938*** | −0.1057493*** | −0.002672 | −0.0128498 | −0.099591*** | 0.0105712 | 0.003222 |
Platform parameters | |||||||||
PlatformLifetime
| −0.0118641*** | −0.0123831*** | −0.011132** | −0.0136595** | −0.0229988*** | −0.0260558*** | |||
Update1
| 1.561665** | 0.96887 | 19.52734*** | 18.02646*** | 21.08901*** | 18.99346*** | |||
Update2
| 3.971721*** | 3.924199*** | −.2991901 | −1.652735 | 3.672342*** | 2.274371* | |||
Update3
| 1.774566*** | 1.370269*** | 3.258874*** | 0.6961245 | 5.033364*** | 2.066448*** | |||
Update4
| −0.8161869*** | −0.3984026 | 1.27061 | 4.795525*** | 0.4548655 | 4.39736*** | |||
Update5
| 1.086508*** | 1.056412*** | −7.615938*** | −7.457788*** | −6.527697*** | −6.397927*** | |||
Update6
| −2.937902*** | −3.147122*** | −3.04403*** | −3.270945*** | −5.981674*** | −6.415,782*** | |||
Update7
| 3.465234*** | 3.204152*** | 8.563072*** | 7.528386*** | 12.02826*** | 10.73,254** | |||
Update8
| 0.6102715*** | 0.7128671*** | 3.106759*** | 2.044481*** | 3.715196*** | 2.756013*** | |||
Update9
| 3.714678*** | 3.994181*** | −8.110425*** | −4.956301*** | −4.394706*** | −.9608749 | |||
Update10
| 1.422225*** | 1.652886*** | 4.824756*** | 5.087945*** | 6.24615*** | 6.739328*** | |||
Seasonal parameters | |||||||||
TVevent1
| −3.454805*** | −17.28362*** | −20.74243*** | ||||||
TVevent2
| 0.7322851*** | 0.1460649 | 0.8795812 | ||||||
Winter
| −0.3442243 | 1.083799* | 0.740641 | ||||||
Spring
| −0.2320078 | 1.421362* | 1.187716 | ||||||
Summer
| 0.1909255 | 4.473041*** | 4.663272*** | ||||||
Constant | 7.894175*** | 47.7862*** | 53.14111*** | 96.13324*** | 55.66326** | 81.10901** | 104.0282*** | 103.4657*** | 134.3192*** |
F
| n/a | n/a | n/a | n/a | n/a | n/a | 94.58 | 134.42 | 148.57 |
Number of observations | 914 | 914 | 914 | 914 | 914 | 914 | 914 | 914 | 914 |
R
2
| 0.0135 | 0.4211 | 0.4429 | 0.2051 | 0.4786 | 0.5530 | 0.1506 | 0.4363 | 0.5215 |
4 Practical application: determining the revenue-optimal share of men and women
4.1 Motivation and numeric example
Variable name | Description | Group 1: men (m) | Group 2: women (w) |
---|---|---|---|
Prob
m
/prob
w
| Basic probability to become a paying user | 6 % | 2 % |
Fee
m
/fee
w
| Avg. fee per paying user | €100 | €100 |
CNE
m
/CNE
w
| Positive CNEs on other user group’s revenue per user | €0.02 | €0.06 |
SNE
m
/SNE
w
| Negative SNEs on same user group’s revenue per user | −€0.015 | −€0.01 |
4.2 User split optimization for the investigated platform
Independent variables | Dependent variable: DailyRevenuePerUser
| ||
---|---|---|---|
Model 1 | Model 2 | Final model 3 | |
User split | |||
ShareOfWomen
| 334.2746*** | 312.4332*** | 346.8351*** |
ShareOfWomenSquared
| −468.437*** | −428.2298*** | −479.6163*** |
Platform parameters | |||
PlatformLifetime
| 0.00136*** | 0.00159*** | |
Update1
| 0.06716 | 0.29307*** | |
Update2
| 0.13269* | −0.27801*** | |
Update3
| −0.25703*** | −0.17709** | |
Update4
| −0.36184*** | −0.14882 | |
Update5
| −0.5221*** | −0.70081*** | |
Update6
| 0.29947*** | −0.05956 | |
Update7
| −0.68634*** | −0.53678*** | |
Update8
| 0.33535** | 0.40668** | |
Update9
| 0.53921*** | 0.69158*** | |
Update10
| 0.21367 | 0.36379* | |
Seasonal parameters | |||
TVevent1
| 0.38896* | ||
TVevent2
| −0.07567 | ||
Winter
| −0.08448 | ||
Spring
| 0.49053*** | ||
Summer
| 0.24884*** | ||
Constant | −56.39442*** | −58.46802*** | −65.29321*** |
F
| 162.70 | 347.90 | 258.91 |
Number of observations | 1005,275 | 1005,275 | 1005,275 |
R
2
| 0.0002 | 0.0034 | 0.0035 |
Optimum (highest revenue dep. on share of women) | 35.7 % | 36.5 % | 36.2 % |
Independent variables | Dependent variable: IsPayer
| ||
---|---|---|---|
Model 1 | Model 2 | Model 3 | |
User split | |||
ShareOfWomen
| 168.1591*** | 198.7777*** | 219.8497*** |
ShareOfWomenSquared
| −232.8991*** | −285.3661*** | −317.5482*** |
Time parameters | |||
PlatformLifetime
| 0.0007249*** | 0.0008232*** | |
UserLifetime
| −0.000601*** | −0.0006021*** | |
Update1
| 0.0038217 | 0.0220544 | |
Update2
| 0.0106529 | −0.0783018** | |
Update3
| −0.0309305 | 0.0075203 | |
Update4
| −0.1802073*** | −0.1577811*** | |
Update5
| −0.0754961** | −0.1610922*** | |
Update6
| 0.1274491*** | 0.0378605 | |
Update7
| −0.1883186*** | −0.1205443*** | |
Update8
| 0.1423438** | 0.1926842*** | |
Update9
| 0.1261103** | 0.1554679*** | |
Update10
| 0.0661558 | 0.0442279 | |
Seasonal parameters | |||
TVevent1
| 0.2236641*** | ||
TVevent2
| −6.59e-06 | ||
Winter
| 0.0374548* | ||
Spring
| 0.1818007*** | ||
Summer
| 0.0576748*** | ||
Constant | −33.53169*** | −40.6881*** | −44.57342*** |
Number of observations | 1005,275 | 1005,275 | 1005,275 |
Pseudo R
2
| 0.0021 | 0.0172 | 0.0175 |
Optimum (highest share of payers dep. on share of women) | 36.1 % | 34.8 % | 34.6 % |