Dynamics of Incentivized Friend Invitationjiwan/paper/2014_kakao_slides.pdf · 5 Anipang 2 for...

Invite Your Friends and Get Rewards: Dynamics of Incentivized Friend Invitation in KakaoTalk Mobile Games

Jiwan Jeong / Sue Moon KAIST COSN’14, Oct 1—2, 2014, Dublin, Ireland

Captured on Oct 1, 2014

Rank Application

1 Taming Monsters for Kakao

2 Clash of Clans

3 Seven Knights for Kakao

4 Everybody’s Marble for Kakao

5 Anipang 2 for Kakao

6 Blade for Kakao

7 Be the Stars for Kakao

8 Cookie Run for Kakao

9 FIFA Online 3

10 Summoners War: Sky Arena

Captured on Jan 1, 2014

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3 Candy Crush Saga for Kakao


5 Pokopang for Kakao

6 Anipang for Kakao

7 Everytown for Kakao

8 KakaoTalk

9 Anipang Mahjong for Kakao

10 Water Margin for Kakao

Top grossing apps on ! Google Play

Captured on Oct 1, 2014

Rank Application


2 Clash of Clans

3 Seven Knights for Kakao


5 Anipang 2 for Kakao

6 Blade for Kakao

7 Be the Stars for Kakao


9 FIFA Online 3

10 Summoners War: Sky Arena

Captured on Jan 1, 2014

Rank Application



3 Candy Crush Saga for Kakao


5 Pokopang for Kakao

6 Anipang for Kakao

7 Everytown for Kakao

8 KakaoTalk

9 Anipang Mahjong for Kakao

10 Water Margin for Kakao

Top grossing apps = KakaoTalk games

KakaoTalk, a mobile instant messenger• De facto standard MIM in Korea

- 37M users among 50M population

- Friendships based on smartphones’ contact book

• KaTalk as a verb in Korea

- Google it!

- FedEx it!

- KaTalk me!

4

Text me! 🙅KaTalk me! 🙆

KakaoTalk’s game platform

5

Gam

es

0

150

300

450

600

Sign

-Ups

0M

150M

300M

450M

600M

July 12 July 13 July 14

Sign-Ups Games

1M users

per game

14 games per user

Behind its rapid growth …• Quota-based reward scheme for friend invitation

- if a user invites 10, 20, and 30 friends cumulatively

- then the user gets reward 💰, 💎, and 🚘, respectively

- no matter whether the invitee signs up or not

6

Inviting friends

7

Inviting friends

8

Quotas and rewards for invitations

Inviting friends

9

List of KakaoTalk friends who did not sign up for

the game yet

Inviting friends

10

Click

Inviting friends

11

Click

Inviting friends

12

Social referrals are not only for games

13

This work• We examine the inviters’ behavior and the invitees’ reaction in

KakaoGame’s quota-based friends invitation

• Then, we see the dynamics of the game diffusion by looking at how the user behavior changes over time

14

Datasets

15

reward quotas user inviter invitee invitation

A 10/20/30 13.4M 7.8M 33.7M 268.1M

B 10/20/30 + 3/5 2.5M 1.3M 17.1M 42.4M

C 10/20/30 + 3/5 0.9M 0.4M 7.6M 12.8M

D 10/20/30 + 5/15/25 0.6M 0.3M 5.0M 7.7M

for 4 games published by Netmarble / for 20 weeks since each game’s release date

Part I Inviters’ behavior

16

Rewards stimulate invitation behavior by …1. Motivating users to invite friends

- What proportion of users invite friends?

2. Pushing motivated users to max out invitations up to quotas

- How many friends do they invite?

17

Rewards stimulate invitation behavior by …1. Motivating users to invite friends

- What proportion of users invite friends? — invitation rate

2. Pushing motivated users to max out invitations up to quotas

- How many friends do they invite? — invitation count

18

Invitation rate and count

19

invitation rate invitation count

user inviter 1Q avg median 3Q

A 100K 87K 30 28.9 30 31

B 100K 40K 20 30.2 30 31

C 100K 32K 20 27.2 30 30

D 100K 31K 20 28.8 30 30

for the first 100K users / for 28 days since each user’s sign-up

Reward is not sufficient to motivate users

20



A 100K 87K 30 28.9 30 31

B 100K 40K 20 30.2 30 31

C 100K 32K 20 27.2 30 30

D 100K 31K 20 28.8 30 30


invitation rates vary corresponding to popularity

of the games

But highly affects the motivated users

21



A 100K 87K 30 28.9 30 31

B 100K 40K 20 30.2 30 31

C 100K 32K 20 27.2 30 30

D 100K 31K 20 28.8 30 30


All games have similar invitation count statistics regardless of popularity

CCDF of invitation counts

22

(a) Game A

CC

DF

1 2 5 20 100 500

0.00

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(b) Game B

CC

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(c) Game C

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(d) Game D

CC

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1 2 5 20 100 500

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Invitation Count

CC

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1 2 5 20 100 500

1e−0

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1 2 5 20 100 500

1e−0

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1 2 5 20 100 500

1e−0

51e−0

31e−0

1Invitation Count

CC

DF

1 2 5 20 100 500

1e−0

51e−0

31e−0

1

Figure 2: CCDF of invitation counts of the first 100, 000 users in the first 28 days after each user’s sign-up.

(a) Game A

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

(b) Game B

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

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(c) Game C

Invitation Count

CC

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1 2 5 20 100 500

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0.75

1.00

(d) Game D

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

Figure 3: CCDF of invitation counts of all users in 20 weeks.

ure 3 we inspect the CCDFs of all users for the full 20 weeksof data. The percentage of users who have sent out equalto or more invitations than the maximum quota in game Adecreases from 80% in Figure 2(a) to 60% in Figure 3(a). Inthe other games with less user growth, the drops are smallerbut still manifest. The later a user joins a game, the morelikely the user’s friends have already signed up for the gameand the more limited the user is in the choices of invita-tions. Thus less percentage of users have fulfilled the max-imum quota of invitations compared to Figure 2. As theinvitation count is reset to 0, users who have reached themaximum quota previously are encouraged to invite more.As a result in game A with reward intervals of 10, additionaldiscontinuations appear between 30 and 60 in Figure 3.2(a).

Many types of human interaction, such as phone calls,e-mails, sexual relationships, and OSN friendships followpower-law distribution [1, 11, 17]. Recent studies of friendinvitation counts report highly skewed distributions similarto power-law [18, 22]. Also, person-to-person product rec-

ommendations show power-law [16]. In our datasets thereare a good number of users who continue to invite beyondthe maximum quota of rewards. Unsurprisingly, the tails ofthe CCDFs in Figures 2 display power-law behavior.

The reward scheme alone does not motivate users to startinviting friends as the proportion of inviters varies from agame to another. Yet, we confirm that the quota-based re-ward scheme is quite effective in pushing users to invite upto the quotas, irrespective of game popularity. That is, mo-tivated users who found the game interesting enough to en-tice friends and made up their minds to invite friends maxout invitations to get rewards. Therefore we conclude thatquota-based reward schemes are effective in exposing thegame to a great user population, often 5x or more than thesigned-up users as shown in Table 2.

3.2 Invitee SelectionNow, how do users select whom to invite? There is a

trade-off between the cost of invitation and reward, where

• Discontinuations at quotas at 20 and 30

• Users max out invitations up to achievable quotas

Motivated users max out their invitations up to achievable quotas. Then, how do inviters select invitees to achieve the quotas?

23

How do users select whom to invite?

• Strategy 1: Users invite same friends to different games

• Strategy 2: Users invite different friends to different games

24

Overlap b/w a user’s invitees in two games• A user’s invitee similarity for a game pair

- u : a user who invites friends to game X and Y

- uX : the set of invitees u invited to game X

- uY : the set of invitees u invited to game Y

25

SuXY =|uX ∩ uY|

min(|uX|, |uY|)

A user’s invitee similarity b/w two games

26

the cost includes emotional pressure for sending unsolicitedmessages to friends. How does a user minimize the cost?Here we present the following two possible strategies.

• Strategy #1: Users invite the same set of friends todifferent games repeatedly, thereby limiting the dam-age to a small circle of friends.

• Strategy #2: Users invite different sets of friends todifferent games, thus spreading the damage widely andimposing less on individual friends.

Which is a more dominant strategy? To answer the ques-tion, we examine the overlap between a user’s invitees be-tween games. For a user u who invites friends to games Xand Y , let uX and uY be the invitees for games X and Y ,respectively. We define the user’s invitee similarity for thegame pair X and Y , Su

XY , as following:

SuXY =

|uX ∩ uY |min (|uX |, |uY |)

Since users cannot invite friends who have already signedup for the game, the invitee selection can be severely re-stricted in popular games. A stands out among the fourgames with its popularity claiming 36% of all KakaoTalkusers. To have a fair comparison of the user’s emotional pres-sure, the two games under examination should have compa-rable rate of adoption. Therefore we exclude the game A inthis analysis and consider only the remaining three.

For every pair of games, we select the users who haveinvited friends in both games. B and C have 179K commoninviters, C and D have 55K, and D and B have 104K. Thenwe calculate Su

XY for all three game pairs. Figure 4 showsthe CCDF of the invitee similarities. For all three gamepairs, about 80% of users invite more than 60% of samefriends to two different games, and for about 50% of usersmore than 80% of invitees are the same. In summary, usersare highly likely to invite the same set of friends to differentgames. Also, the distributions of users’ invitee similarity forall three game pairs are analogous to each other.

Invitee Similarity Between Games

Invitee Similarity

CC

DF

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

B and CC and DD and B

Figure 4: CCDF of invitee similarity.

Our observation above supports Strategy #1, but why dopeople use Strategy #1? One possible explanation is thatgamers’ preference to those games are similar. To exam-ine the preference similarity among games, we compute the

member and inviter overlaps between games as follows. LetMXY be the member similarity and IXY be the inviter sim-ilarity between games X and Y ,

MXY =|MX ∩MY |

min (|MX |, |MY |) , IXY =|IX ∩ IY |

min (|IX |, |IY |)

where MG is the set of members in game G, and IG is theset of inviters in game G. Not all members have invitedfriends, and thus MG ⊃ IG.

Table 4 summarizes the member similarities and invitersimilarities among the three games, and compares them withaverage invitee similarities. The member and inviter simi-larities vary from a low of 0.2651 to a high of 0.5891. Yet,the average invitee similarity remains high, over 0.7. There-fore, we conclude that users invite the same set of friends,regardless of the preference for games.

X Y MXY IXY Avg. SuXY

B C 0.5214 0.4544 0.7529C D 0.3280 0.2177 0.7388D B 0.5891 0.2651 0.7022

Table 4: Similarities between games.

For the curiosity for the personal motivation behind Strat-egy #1, we conducted an informal survey among 50 gamersand 47 of them answered that they invite closest friends re-gardless of the game. We leave a rigorous user study for themotivation for future work.

3.3 Mental Mechanics of InvitersIf you are a compensation plan designer for a WOM mar-

keting campaign with quota-based rewards, setting a properquota is critical for the success. Too low a quota, for ex-ample, 5 friends to invite for the reward, may not bringenough exposure. On the other hand, too high a quota, forexample 100, may actually discourage users and lead themto abandon the effort altogether. We investigate the time ittakes for a user to invite friends to understand the mentalmechanics of inviters.

In the previous section we have seen that most users in-vite the same set of close friends repeatedly. Then how bigis the circle of close friends? Or to put it differently, howlong does a person take to name the close friends? From thelogs we mine the timestamps between invitations and plotthem in Figure 5. The data points are grouped in 5 alongthe x-axis. The y-axis is the inter-invitation time betweentwo consecutive invitations. The boxes represent the quar-tiles and the upper and lower marks represent the 5 and 95percentiles of the inter-invitation time. Results from all fourgames are very similar, and here we only present the resultsfrom A.

Figure 5(a) pictures the inter-invitation time evolution ofthose who invited exactly 20 friends. The inter-invitationtime dips if very minutely from the 5-th to the 10-th invi-tee in all three figures in Figure 5. We believe this slightdecrease in invitation time is likely to be due to user’s im-proved familiarity with the invitation mechanism. A con-spicuous jump in the 95-percentile takes place from the 15-th to 20-th invitee in Figure 5(a). A bigger jump is from the20th to 25-th in Figure 5(b). In Figure 5(b) the third quar-tile and median also increase, representing the extra mentalcost users experience in listing 10 more friends beyond 20.

Users invite same friends to different games

27





XY , as following:

SuXY =

|uX ∩ uY |min (|uX |, |uY |)





Invitee Similarity

CC

DF

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0





MXY =|MX ∩MY |

min (|MX |, |MY |) , IXY =|IX ∩ IY |

min (|IX |, |IY |)




B C 0.5214 0.4544 0.7529C D 0.3280 0.2177 0.7388D B 0.5891 0.2651 0.7022







Users invite same friends to different games

28





XY , as following:

SuXY =

|uX ∩ uY |min (|uX |, |uY |)





Invitee Similarity

CC

DF

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

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1.0





MXY =|MX ∩MY |

min (|MX |, |MY |) , IXY =|IX ∩ IY |

min (|IX |, |IY |)




B C 0.5214 0.4544 0.7529C D 0.3280 0.2177 0.7388D B 0.5891 0.2651 0.7022







Users invite closest friends to regardless of the game

29

6%

94%

I invite my closest friends regardless of the gameI don't

informal survey among 50 gamers

Most users invite the same set of close friends repeatedly to different games. Then how big is the circle of close friends?

30

Setting a proper quota is important

Invite 5 friends and get rewards! — Not enough exposure

Invite 100 friends and get rewards! — Discourage users

How many friends a user can invite comfortably?

Our approach — How long does it take to select xth invitee?

31

Times it takes to select x-th invitee

32

* for those who invite exactly 30 friends in A

(a) Who Invite 20 Friends

x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20

(b) Who Invite 30 Friends

x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30

(c) Who Invite 40 or More Friends

x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30 35 40

Figure 5: Time it takes an inviter to select x-th invitee in A. (a) For those who invited exactly 20 friends.(b) For those who invited exactly 30 friends. (c) For those who invited 40 or more friends. The x-axis isgrouped in units of 5. The boxes represent the quartiles and the upper and lower marks represent the 5 and95 percentiles.

(a) Game A

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

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(b) Game B

Invitation Count

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reset 0reset 1reset 2

(c) Game C

Invitation Count

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(d) Game D

Invitation Count

CC

DF

0 10 20 30 40 500.

00.

20.

40.

60.

81.

0

Figure 6: Weekly CCDF of the invitation counts. Black lines for the weeks before the first reward reset, redlines for after the first reward reset, and green lines for the weeks after the second reward reset for B (bestviewed in color).

Apparently, those who invite beyond the maximum re-ward quota feel much less pressure about friend invitation.In Figure 5(c) for those who invite 40 or more friends, theselection time is much lower than the previous groups. Nev-ertheless, there is also a slight bump after 20. Thus weconclude that there is a mental hurdle somewhere between21 to 30 in naming close friends.

Another angle to study the inviter’s mental mechanics isto see the reaction to the quota over time. How has theuser’s invitation behavior changed? As more users sign upfor the game over time, there remain fewer users to invite.Thus the number of friends a user invites should decreaseover time. Is the change incremental? Figure 6 show theweekly CCDF of the invitation counts. As all games havehad reward resets, we use black lines for weeks before thereset, and red for after.

During the course of our log collection, B had reset thequota in the 11th week and reset again with its maximumquota change from 30 to 40 in the 15th week. For B, we usea third color green for the weeks after the second reset.

For A, C, and D, graphs in black or weeks before thereset tend to be above the red lines. That is, the earlierusers invite friends, the more they invite. In the case of B,we see a stark drop for the graphs in green. Since the secondreset, almost no one has the heart to invite up to the quotaand gave up around 20.

It is too premature to draw a conclusion on the mentalcapacity for human social networking from this data alone,and we only note the above as interesting observations thatrequire further study.

4. INVITEE’S REACTIONFriend invitations arrive unsolicited, and that alone could

trouble the invitee, whether it comes from a close friend ornot. Worse yet, a user may get multiple invitations to thesame game. It would be interesting to understand the user’sreaction to multiple invitations. In this section, we analyzethe invitee’s reaction in 10,000 sampled invitees in C.

The response to social referrals has been studied in a fewplatforms, but the results are not consistent. In an onlineretailer’s referral program, the probability of buying a book

Users invite up to 20 friends comfortably

33

* for those who invite exactly 30 friends in A


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30 35 40


(a) Game A

Invitation Count

CC

DF

0 10 20 30 40 50

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Invitation Count

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(c) Game C

Invitation Count

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Invitation Count

CC

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0 10 20 30 40 500.

00.

20.

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81.

0










Mr. Dunbar’s circles of acquaintanceship

150 — just friends

50 — trusted friends

15 — good friends

5 — best friends

34

Robin Dunbar, How Many Friends One Person Need? (2010), Harvard University Press

Our social circle size for incentivized WOM

20 friends for comfortable

invitation

150 — just friends

50 — trusted friends

15 — good friends

5 — best friends

35

Part 1 Summary• In the quota-based reward schemes

- The quotas affect motivated users to max out invitations

- The invitations spread through the closest friendships

- The social circle size for comfortable invitation is 20

36

Part 2 Invitees’ reaction

37

How do invitees react to multiple incoming invitations?

38

Different results from previous workProbability of buying a book (Leskovec et al., EC’06)

39

Different results from previous workProbability of adopting a health behavior (Centola, Science, 2010)

40

Different results from previous workProbability of joining a Facebook game (Wei et al., WOSN’10)

41

Time intervals b/w invites are critical to sign-up

42

peaks at receiving two recommendations and then drops [16].In an online social network experiment, the probability ofadopting a health community activity increases up to foursocial signals [6]. In a social game diffusion case on Face-book, the probability of joining a game steadily increases asone gets more invitations [22].

All of the above studies only consider the number of in-coming invitations per user. Yet, the temporal aspect in theinvitation is another important factor. Receiving a num-ber of invitations in a short period of time may be moreattractive than receiving them staggered over time. Fig-ure 7 shows the probability of signing up for C after re-ceiving x invitations over time. When we do not considerthe time interval between incoming invitations, the proba-bility of joining decreases as one receives more invitationsas in Figure 7(a), which is consistent to Leskovec et al.’sobservation [16]. However, if we set the limit to a week,the probability of signing up for the game increases up toreceiving 4 invitations, supporting Centola’s observation [6].

(a) Total

Number of Incoming Invitations

Prob

. of S

igni

ng U

p

1 2 3 4 5 6

0.0

0.2

0.4

0.6

(b) A Week

Number of Incoming Invitations

Prob

. of S

igni

ng U

p

1 2 3 4 5 6

0.0

0.2

0.4

0.6

Figure 7: Probability of signing up given a numberof incoming invitations for C. (a) In total. (b) In aweek.

In Figure 7 we see that the time intervals between in-coming invitations play a key role as well as the number ofincoming invitations. In order to study the temporal aspectof invitations, we define p(n, d) as the ratio of those who signup over the total number of people who received exactly ninvitations spanning d days. Then, p(1, 1) means the ratioof sign-ups among invitees who received only one invitation.If p(n, d) > p(1, 1), sending an invitation message to an in-vitee who received n − 1 invitations within d days is moreeffective than inviting a new person. If p(n, d) < p(n−1, d),sending n-th invitation to an invitee is not that effective.

Table 5 shows p(n, d) values, where the rows represent nand columns represent d. The first observation from the ta-ble is in a row the values increase when d decreases from rightto left: invitations are more persuasive when they arrive ina shorter time span. Or for the same number of invitations,the longer it takes to receive them, the less likely the usersigns up. At what point does it become not worthwhile tosend an additional invitation? Using p(1, 1) as the cut-offpoint, the dark shaded area represent the region of not effec-tive invitation. If an additional invitation does not amountto the marginal utility of p(1, 1), the invitation might as wellbe spent on a user never invited before.

More invitations for the same period of time do not alwayshave a positive effect on the invitee. Except for d = 1, ifthe number of invitations goes over 4, the probability ofsign-up starts to decrease. Why four invitations? Either

d1 2 3 4 5 ≥6

n

1 10.0 - - - - -2 29.2 23.2 12.3 9.2 6.8 2.93 83.3 20.7 16.7 12.2 6.7 2.04 100.0 88.9 50.0 20.0 25.0 2.25 100.0 85.7 20.0 - - -

Table 5: Table of p(n, d), the percentage of thosewho sign up over the total number of people whoreceived exactly n invitations spanning d days. Theshaded area represents not effective invitations.

by coincidence or not, our number is consistent with thatreported by Centola [6]. We envision the need for controlledexperiments to verify the psychological threshold of four andleave it for future work.

Based on the observations in this section, game compa-nies can improve the effectiveness of friend invitations. Forexample, they can put recently invited people on top of thefriend list as long as they have fewer than four invitationsfrom friends. As time passes and if a user has received fourinvitations or more, the user should be demoted off the topin the friend’s list of the recommended.

5. PROPAGATION SPEEDPrevious sections describe how inviters and invitees be-

have in the quota-based reward schemes. Now we begin toexamine how quickly the invitations are sent out and prop-agated. Our datasets are well suited for the study of gamepropagation, because the invitation and the act of sign-upare both explicit and timestamped with millisecond accu-racy. In this section, we investigate the diffusion speed ofgame C. We divide the invitation cascading process intothree phases, and examine the distributions of the time in-tervals for the three stages.

• t1: Time interval from receiving an invitation to join-ing the game. (If a user received multiple invitations,we consider only the last one.)

• t2: Time interval from joining the game to sending thefirst invitation.

• t3: Time interval between consecutive invitations sentby a user.

We plot the distribution of each time interval in Figure 8.In Figure 8(a) about 20% of the sign-ups occurred within anhour after the last invitation received, 50% occurred within aday, and 80% occurred within a week. It seems like the CDFis linearly proportional to logarithm of the time intervals,F (t1) ∝ log t1, implying P (t1) ∝ 1/t1.

After joining a game, users start inviting in very quicksuccession. As shown in Figure 8(b), about 50% of invitersstart inviting friends within 5 minutes after joining the game,while only about 20% of users invite friends half a day aftersign-ups. Most of the users invite friends right after thetutorial or a few additional plays.

After sending the first invitation, the users send consecu-tive invitations in a bursty manner. In Figure 8(c), about50% of the invitations occurred within 6 seconds from theprevious one, and more than 90% occurred within 1 minute.

*10000 sampled invitees in game C

We define p(n,d)• p(n,d) to be …

- the percentage of signed-ups users among

those who received n invitations spanning d days

*d = time interval between the first and the last invitations

43

p(n, d) =# sign-ups among them

# those who received n invites spanning d days

Table of p(n,d)

44

d

1 2 3 4 5 >=6

n

1 10.0 - - - - -

2 29.2 23.2 12.3 9.2 6.8 2.9

3 83.3 20.7 16.7 12.2 6.7 2.0

4 100.0 88.9 50.0 20.0 25.0 2.2

5 100.0 85.7 20.0 - - -

for 10K sampled users in game C

d

1 2 3 4 5 >=6

n

1 10.0 - - - - -

2 29.2 23.2 12.3 9.2 6.8 2.9

3 83.3 20.7 16.7 12.2 6.7 2.0

4 100.0 88.9 50.0 20.0 25.0 2.2

5 100.0 85.7 20.0 - - -


Shorter intervals, more likely to sign up

45

d

1 2 3 4 5 >=6

n

1 10.0 - - - - -

2 29.2 23.2 12.3 9.2 6.8 2.9

3 83.3 20.7 16.7 12.2 6.7 2.0

4 100.0 88.9 50.0 20.0 25.0 2.2

5 100.0 85.7 20.0 - - -


Up to 4 invitations, more likely to sign up

46

d

1 2 3 4 5 >=6

n

1 10.0 - - - - -

2 29.2 23.2 12.3 9.2 6.8 2.9

3 83.3 20.7 16.7 12.2 6.7 2.0

4 100.0 88.9 50.0 20.0 25.0 2.2

5 100.0 85.7 20.0 - - -


Up to 4 invitations, more likely to sign up

47

d

1 2 3 4 5 >=6

n

1 10.0 - - - - -

2 29.2 23.2 12.3 9.2 6.8 2.9

3 83.3 20.7 16.7 12.2 6.7 2.0

4 100.0 88.9 50.0 20.0 25.0 2.2

5 100.0 85.7 20.0 - - -


p(1,1) can be cut-off value for effectiveness

48

p(1,1) = sign-ups among invitees who received only one invitation


'

a new invitee

(

2 invites in 3 days

49


'

a new invitee

p(1,1) = 10.0%

(

2 invites in 3 days

p(2+1,3+1) = 12.2%

50

<


'

a new invitee

p(1,1) = 10.0%

(

2 invites in 3 days

p(2+1,3+1) = 12.2%

more effective!

51

<


'

a new invitee

p(1,1) = 10.0%

more effective!

)

2 invites in 4 days

p(2+1,4+1) = 6.7%

52

>

d

1 2 3 4 5 >=6

n

1 10.0 - - - - -

2 29.2 23.2 12.3 9.2 6.8 2.9

3 83.3 20.7 16.7 12.2 6.7 2.0

4 100.0 88.9 50.0 20.0 25.0 2.2

5 100.0 85.7 20.0 - - -



53

Part 2 Summary• When a user receives multiple invitations

- Time intervals are important as well as the # of invitations

- More than 4 invitations are not persuasive

✴ Use p(n,d) table for the utility of an invitation

54

Part 3 Causes for Saturation

55

Diffusion explodes and terminates quickly

56

Dataset Statistics Reward Schemesnuser ninviter ninvitee ninvitation Reward Quotas Reward Resets Notes

A 13, 413K 7, 762K 33, 668K 268, 123K 10/20/30 15th weekB changed the quotasto 5/10/20/30/40 atthe 2nd reward reset

B 2, 510K 1, 270K 17, 111K 42, 419K 3/5/10/20/30 11th & 15th weeksC 872K 393K 7, 567K 12, 816K 3/5/10/20/30 6th weekD 648K 253K 4, 934K 7, 680K 5/10/15/20/25/30 6th week

Table 2: Dataset statistics and reward schemes.

(a) Game A

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

Sign−UpsInvitations

(b) Game B

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

(c) Game C

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

(d) Game D

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

Figure 1: Weekly new sign-ups and invitations.

2.3 Friend Invitation and User GrowthKakaoGame has won its fame for its fast user growth

mechanism. Figure 1 plots the weekly numbers of new sign-ups and invitations of the four games. The two numbers arehighly correlated; the Pearson correlation coefficient is 0.94.Both numbers are the highest during the first week of thegame release. In case of A, 4 million users joined the gameand sent out 58 million invitations only in the first week.In contrast to the explosive growth in the early stage, bothnumbers drop exponentially (the y-axis of the graph is in logscale) over time. The dotted vertical lines represent rewardresets. Even with the reward resets, the numbers of invita-tions and new sign-ups decrease by two orders of magnitudein 20 weeks after the initial release.

How does the quota-based reward scheme bring explosiveuser growth in the beginning? How does the user growthslow down exponentially over time? How do the invitersand invitees affect the diffusion dynamics? We answer thesequestions one by one in the following sections.

3. INVITER’S BEHAVIOR

3.1 Invitation Rate and CountHow do the quota-based reward schemes affect the invita-

tion behavior? We begin by examining the invitation rate,the proportion of inviters among signed-up users, and the in-vitation count, the number of friends an inviter invites to agame. The reward scheme is not the only factor that affectsthe invitation behavior. For example, the player populationof a game can limit invitation because users cannot invitefriends who already signed up. Also, the reward resets thatclear the quotas can stimulate invitations by encouragingusers who have reached the maximum quota previously.

To observe the invitation behavior at an early stage withno reward reset, we use only the first 28 days of data afterthe sign-up for the first 100,000 users. Table 3 summarizesthe statistics. The invitation rates vary from a low of 30%

Invitation Rate Invitation Countnuser ninviter 1Q Avg. Med. 3Q

A 100K 87K 30 28.9 30 31B 100K 40K 20 30.2 30 31C 100K 32K 20 27.2 30 30D 100K 31K 20 28.8 30 30

Table 3: Invitation rate and count statistics fromthe first 28 days of data after the sign-up for thefirst 100,000 users.

to a high of 90%, corresponding to popularity of the games.However, all the games show similar invitation count statis-tics, as they have similar reward schemes. For all four games,the median of invitation count is exactly 30, and the aver-age and the 3rd quartile are also around 30, which is themaximum quota.

In Figure 2, we plot the complementary cumulative dis-tribution function (CCDF) of the invitation count for eachgame. The CCDFs show marked discontinuations at quotasof the games. A is the most popular game with the total of13 million signed-up users, and 75% of its users sent out themaximum quota or more. In all four games, more than halfof the inviters have sent out equal to or more invitations thanthe maximum quota of 30. Beyond the maximum quota, Aoffers no more reward, while the other games give away acoin2 per invitation. Possibly due to the coins, games otherthan A have heavy inviters who sent out hundreds of invi-tations.

So far, we have seen the invitation behavior at the earlystage. How does the invitation behavior change over time,with growing gamer population and reward resets? In Fig-

2Users play a game with a coin. (Usually,) a user gets a freecoin every 10 minutes, but cannot accumulate more than5 coins at any point. When a user runs out of coins, theuser must wait until a refill or purchase coins to continueplaying.

There are still millions of people who didn’t sign up for the games. But why does it spread no more?

57

Diffusion = Decisions

58

Whether or not to invite

friends?

How many friends to

invite?

Whether or not to join the game?

How these decisions change over time?

Causes for Saturation

• As time passes …

Possibility 1 — New sign-ups do not invite friends as before

Possibility 2 — New inviters invite fewer friends than before

Possibility 3 — New invitees do not sign up for the game

59

Constant % of new sign-ups invite friends

60

(a) Invitation Rate

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

(b) Average Invitation Count

Weeks since Release

Aver

age

Invi

tatio

n C

ount

2 4 6 8 10

05

1015

2025

30

(c) Acceptance Rate

Days since Release

Acce

ptan

ce R

ate

5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

0.6

among all inviteesamong new invitees

Figure 9: Time series showing the changes in the diffusion statistics of C. (a) The proportion of inviters amongnew sign-ups. (b) The average number of invitations a new inviter sent during a week. (c) The proportionof sign-ups among invitees. We plot the acceptance rate in daily binning to show its rapid decrease.

(a) Game A

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(b) Game A

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(c) Game B

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(d) Game B

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(e) Game D

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(f) Game D

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

Figure 10: Time series showing the diffusion statis-tics of A, B, and D. (left) The proportion of invitersamong new sign-ups. (right) The average number ofinvitations a new inviter sent during a week.

drop as the invitations spread through the network. Even-tually, most of the incentivized friend invitation cascadingterminates. Nevertheless, it is efficient and effective becauseit draws a large number of people explosively at the earlystage of a game launch.

7. RELATED WORKWOMmarketing is attracting massive interest with emerg-

ing social platforms, but studies on the influence of WOMgo as far back as decades. Earliest studies on WOM effectwere survey-based, and reported that WOM affects not onlypurchase decisions, but also pre- and post-purchase percep-tions [2, 12, 14]. Recently, the survey-based work begins tofocus on the online and, in particular, the mobile environ-ment [10, 20].

As OSNs have emerged providing venues for content shar-ing, a number of studies characterized content dissemina-tion on OSNs. Guhl et al. studied information diffusionon blogspace based on keywords and links [13]. Cha et al.investigated the photo propagation on Flickr from favoritemarking activities [7]. However, these works have limitationthat they infer WOM rather than directly observe it.

Investigating direct WOM is rare because of the lack inpublic data. Leskovec et al., reported an analysis of person-to-person recommendation via e-mail on an online retailer,as the first empirical study with large-scale data [16]. On theother hand, Centola designed an experiment about spread ofbehavior on artificially generated social networks [6]. Withthe recent advent of social platforms based on existing socialnetworks such as Facebook, Wei et al., studied diffusion ofsocial games on Facebook platform via friend invitation [22].

8. CONCLUSIONSIn this paper, we analyze the user behavior and diffusion

dynamics in friend invitation programs compensated withquota-based rewards.

The incentives motivate users to invite their friends up toreward quotas, only beyond which we start to see power-lawtail behavior. Users tend to invite their closest friends todifferent genres of games, regardless of the game popularityor one’s own preference. In general, users invite 20 friendscomfortably.

… and they invite a similar # of friends

61

(a) Invitation Rate

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Weeks since Release

Aver

age

Invi

tatio

n C

ount

2 4 6 8 10

05

1015

2025

30

(c) Acceptance Rate

Days since Release

Acce

ptan

ce R

ate

5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

0.6



(a) Game A

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(b) Game A

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(c) Game B

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(d) Game B

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(e) Game D

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(f) Game D

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40










Invitees’ acceptance rate drops rapidly

62

(a) Invitation Rate

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Weeks since Release

Aver

age

Invi

tatio

n C

ount

2 4 6 8 10

05

1015

2025

30

(c) Acceptance Rate

Days since Release

Acce

ptan

ce R

ate

5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

0.6



(a) Game A

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(b) Game A

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(c) Game B

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(d) Game B

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(e) Game D

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(f) Game D

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40










Effect of old invitees? NoHomophily? Possibly…

Summary• We study the friend invitation in KakaoTalk games

• The diffusion explodes at the beginning and soon decay

• Invitations spread through closest friendships

- Social circle size for comfortable invitation is 20

- Persuasive incoming invitation size is 4

- Rapid drop in acceptance rate leads termination of diffusion

63

a mobile game analytics startup that launched in April this year, has been

acquired at $40M by

Weekly new sign-ups and invitations

66

Dataset Statistics Reward Schemesnuser ninviter ninvitee ninvitation Reward Quotas Reward Resets Notes

A 13, 413K 7, 762K 33, 668K 268, 123K 10/20/30 15th weekB changed the quotasto 5/10/20/30/40 atthe 2nd reward reset

B 2, 510K 1, 270K 17, 111K 42, 419K 3/5/10/20/30 11th & 15th weeksC 872K 393K 7, 567K 12, 816K 3/5/10/20/30 6th weekD 648K 253K 4, 934K 7, 680K 5/10/15/20/25/30 6th week

Table 2: Dataset statistics and reward schemes.

(a) Game A

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

Sign−UpsInvitations

(b) Game B

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

(c) Game C

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

(d) Game D

Weeks since Release

New

Sig

n−U

ps &

Invi

tatio

ns

5 10 15 20

1e+0

21e

+04

1e+0

61e

+08

Figure 1: Weekly new sign-ups and invitations.

2.3 Friend Invitation and User GrowthKakaoGame has won its fame for its fast user growth

mechanism. Figure 1 plots the weekly numbers of new sign-ups and invitations of the four games. The two numbers arehighly correlated; the Pearson correlation coefficient is 0.94.Both numbers are the highest during the first week of thegame release. In case of A, 4 million users joined the gameand sent out 58 million invitations only in the first week.In contrast to the explosive growth in the early stage, bothnumbers drop exponentially (the y-axis of the graph is in logscale) over time. The dotted vertical lines represent rewardresets. Even with the reward resets, the numbers of invita-tions and new sign-ups decrease by two orders of magnitudein 20 weeks after the initial release.

How does the quota-based reward scheme bring explosiveuser growth in the beginning? How does the user growthslow down exponentially over time? How do the invitersand invitees affect the diffusion dynamics? We answer thesequestions one by one in the following sections.

3. INVITER’S BEHAVIOR

3.1 Invitation Rate and CountHow do the quota-based reward schemes affect the invita-

tion behavior? We begin by examining the invitation rate,the proportion of inviters among signed-up users, and the in-vitation count, the number of friends an inviter invites to agame. The reward scheme is not the only factor that affectsthe invitation behavior. For example, the player populationof a game can limit invitation because users cannot invitefriends who already signed up. Also, the reward resets thatclear the quotas can stimulate invitations by encouragingusers who have reached the maximum quota previously.

To observe the invitation behavior at an early stage withno reward reset, we use only the first 28 days of data afterthe sign-up for the first 100,000 users. Table 3 summarizesthe statistics. The invitation rates vary from a low of 30%

Invitation Rate Invitation Countnuser ninviter 1Q Avg. Med. 3Q

A 100K 87K 30 28.9 30 31B 100K 40K 20 30.2 30 31C 100K 32K 20 27.2 30 30D 100K 31K 20 28.8 30 30

Table 3: Invitation rate and count statistics fromthe first 28 days of data after the sign-up for thefirst 100,000 users.

to a high of 90%, corresponding to popularity of the games.However, all the games show similar invitation count statis-tics, as they have similar reward schemes. For all four games,the median of invitation count is exactly 30, and the aver-age and the 3rd quartile are also around 30, which is themaximum quota.

In Figure 2, we plot the complementary cumulative dis-tribution function (CCDF) of the invitation count for eachgame. The CCDFs show marked discontinuations at quotasof the games. A is the most popular game with the total of13 million signed-up users, and 75% of its users sent out themaximum quota or more. In all four games, more than halfof the inviters have sent out equal to or more invitations thanthe maximum quota of 30. Beyond the maximum quota, Aoffers no more reward, while the other games give away acoin2 per invitation. Possibly due to the coins, games otherthan A have heavy inviters who sent out hundreds of invi-tations.

So far, we have seen the invitation behavior at the earlystage. How does the invitation behavior change over time,with growing gamer population and reward resets? In Fig-

2Users play a game with a coin. (Usually,) a user gets a freecoin every 10 minutes, but cannot accumulate more than5 coins at any point. When a user runs out of coins, theuser must wait until a refill or purchase coins to continueplaying.

CCDF of invitation counts

67

(a) Game A

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

(b) Game B

CC

DF

1 2 5 20 100 5000.

000.

250.

500.

751.

00

(c) Game C

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

(d) Game D

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

Invitation Count

CC

DF

1 2 5 20 100 500

1e−0

51e−0

31e−0

1

Invitation Count

CC

DF

1 2 5 20 100 500

1e−0

51e−0

31e−0

1

Invitation CountC

CD

F

1 2 5 20 100 500

1e−0

51e−0

31e−0

1

Invitation Count

CC

DF

1 2 5 20 100 500

1e−0

51e−0

31e−0

1

Figure 2: CCDF of invitation counts of the first 100, 000 users in the first 28 days after each user’s sign-up.

(a) Game A

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

(b) Game B

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

(c) Game C

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

(d) Game D

Invitation Count

CC

DF

1 2 5 20 100 500

0.00

0.25

0.50

0.75

1.00

Figure 3: CCDF of invitation counts of all users in 20 weeks.

ure 3 we inspect the CCDFs of all users for the full 20 weeksof data. The percentage of users who have sent out equalto or more invitations than the maximum quota in game Adecreases from 80% in Figure 2(a) to 60% in Figure 3(a). Inthe other games with less user growth, the drops are smallerbut still manifest. The later a user joins a game, the morelikely the user’s friends have already signed up for the gameand the more limited the user is in the choices of invita-tions. Thus less percentage of users have fulfilled the max-imum quota of invitations compared to Figure 2. As theinvitation count is reset to 0, users who have reached themaximum quota previously are encouraged to invite more.As a result in game A with reward intervals of 10, additionaldiscontinuations appear between 30 and 60 in Figure 3.2(a).

Many types of human interaction, such as phone calls,e-mails, sexual relationships, and OSN friendships followpower-law distribution [1, 11, 17]. Recent studies of friendinvitation counts report highly skewed distributions similarto power-law [18, 22]. Also, person-to-person product rec-

ommendations show power-law [16]. In our datasets thereare a good number of users who continue to invite beyondthe maximum quota of rewards. Unsurprisingly, the tails ofthe CCDFs in Figures 2 display power-law behavior.

The reward scheme alone does not motivate users to startinviting friends as the proportion of inviters varies from agame to another. Yet, we confirm that the quota-based re-ward scheme is quite effective in pushing users to invite upto the quotas, irrespective of game popularity. That is, mo-tivated users who found the game interesting enough to en-tice friends and made up their minds to invite friends maxout invitations to get rewards. Therefore we conclude thatquota-based reward schemes are effective in exposing thegame to a great user population, often 5x or more than thesigned-up users as shown in Table 2.

3.2 Invitee SelectionNow, how do users select whom to invite? There is a

trade-off between the cost of invitation and reward, where

Time it takes an inviter to select x-th invitee

68


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30 35 40


(a) Game A

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

(b) Game B

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0


(c) Game C

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

(d) Game D

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0










Weekly CCDF of invitation counts

69


x−th InviteeSe

lect

ion

Tim

e (s

ec)

05

1015

2025

5 10 15 20


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30


x−th Invitee

Sele

ctio

n Ti

me

(sec

)

05

1015

2025

5 10 15 20 25 30 35 40


(a) Game A

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

(b) Game B

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0


(c) Game C

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

(d) Game D

Invitation Count

CC

DF

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0










Timing of invitation cascading

70

(a) Invitation to Sign−Up

t1

CDF

5m 1h 1d 1w

0.0

0.2

0.4

0.6

0.8

1.0

(b) Sign−Up to Invitation

t2

CDF

5m 1h 12h 1w

0.0

0.2

0.4

0.6

0.8

1.0

(c) Inter−Invitation

t3

CDF

6s 1m 1h 1d

0.0

0.2

0.4

0.6

0.8

1.0

(d) Inter−Invitation

t3 (second−bin)

PDF

6s 1m 1h 1d

1e−07

1e−05

1e−03

1e−01

Figure 8: Timing of invitation cascading. (a) Time interval from receiving an an invitation to joining thegame. (b) Time interval from joining the game to sending the first invitation. (c), (d) Time interval betweenconsecutive invitations sent by a user.

As shown in Figure 8(d), the PDF of t3 follows power-law, indicating that an individual’s invitation pattern hasa bursty nature. Barabasi models the bursty nature of hu-man activities as a priority-based decision process [3]. Inquota-based reward schemes, invitations up to reward quo-tas have high priority than the remainders. Users send sev-eral invitations during a single session in quick successionto meet the reward quotas, followed by a long period of noinvitation activity. The immediate and bursty nature of theinvitation behavior can be explained by the law of dimin-ishing marginal utility. The utility of a reward is greater atthe beginning of the game playing, because users have lim-ited ability and experience to earn commodity such as gamemoney or items.

Quota-based reward schemes not only motivate users toinvite many friends, but also spur the pace of its propaga-tion. This makes the explosive growth of the games at thevery early stage, as we have witnessed new sign-ups and in-vitations occur in an explosive manner in the first week ofthe game launch as Figure 1.

6. CAUSES FOR SATURATIONIn previous sections we have learned that friend invitations

are a very effective mechanism for game advertisement andrecruiting. However, the user growth soon reaches satura-tion regardless of the popularity (in Figure 1, new sign-upsdecrease exponentially). Earlier studies characterize whatdrives ongoing WOM [4, 8, 10, 20], but none of them inves-tigate what causes its termination. There are still millions ofpeople not yet registered for the services, but why does theWOM spread no more? In this section, we study the causesfor slowdown in the diffusion of the games, using data C.

The diffusion of the games arises from aggregation of eachindividual’s decisions about the invitation. There are threedecision points an individual faces. First, after signing upand playing a few matches, the user decides whether or notto invite friends. Then, the user decides whom and howmany friends to invite. In next turn, each of the inviteesdecides whether or not to sign up for the game, and if so,the decision process repeats. To reveal where the slowdownoccurs most at among the three decision points, we look atthe temporal changes of the following measures.

• Invitation rate: what proportion of the signed-up usersstart inviting friends?

• Average invitation count : how many friends do theinviters invite on average?

• Acceptance rate: what proportion of the invitees actu-ally sign up for the game?

Figure 9 shows the temporal changes of the invitation rateand the average invitation count for 10 weeks, and the ac-ceptance rate for 3 weeks in C. Surprisingly, whenever usersjoined the game, constant proportion (mean = 0.48, sd =0.04) of the users start inviting friends as in Figure 9(a).Also they invite a similar number (mean = 24.21, sd = 1.32)of friends on average as in Figure 9(b). However, the accep-tance rate drops dramatically by the day. Invitees who didnot sign up for the game are continuously exposed to addi-tional invitations, while the signed-up invitees are not. Thismay cause the decreasing acceptance rate. Thus, we plotthe acceptance rates for all invitees and new invitees whoreceived the first invitation separately in Figure 9(c), andthe acceptance rates for both groups drop rapidly.

With the sampled data, we could only check the accep-tance rate for C. However, we show the time series of theinvitation rate and the average invitation count of the othergames in Figure 10. In A, the invitation rate decreases from0.8 to 0.4, but still a significant proportion of users actuallyinvite friends. The decreases in A arise from its popularity.Because most of the people have already signed up for thegame, the users have limited friends to invite. Other gamesshows similar patterns to C, resulting in constant invitationrates and average invitation counts for ten weeks.

The result is striking because of the decrease in accep-tance rate brings all the slowdown of diffusion. It is naturalto expect that the termination of diffusion comes from acombination of three factors, but our analysis result pointsat only the acceptance rate.

One possible explanation for this result is homophilic na-ture of social network formation. In this incentivized WOMreferral program, users invite closest friends as we have seenin Section 3.2. The diffusion of games may be initiated bya small number of the game fans at the beginning. Theirclose friends are likely to have similar preferences, and theyare likely to accept the invitation. However the preferences

(a) Invitation Rate

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Weeks since Release

Aver

age

Invi

tatio

n C

ount

2 4 6 8 10

05

1015

2025

30

(c) Acceptance Rate

Days since Release

Acce

ptan

ce R

ate

5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

0.6



(a) Game A

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(b) Game A

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(c) Game B

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(d) Game B

Weeks since Release

Avg.

Invi

tatio

n C

ount

2 4 6 8 10

010

2030

40

(e) Game D

Weeks since Release

Invi

tatio

n R

ate

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

(f) Game D

Weeks since ReleaseAv

g. In

vita

tion

Cou

nt

2 4 6 8 10

010

2030

40Figure 10: Time series showing the diffusion statis-tics of A, B, and D. (left) The proportion of invitersamong new sign-ups. (right) The average number ofinvitations a new inviter sent during a week.









Invitation rates and counts over time

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