Do Online Game
Players Overplay?
Dan Acland and Vinci Chow
14th October 2008
Motivation

Internet/Video Game overplaying is an increasing concern

American Time Use Survey 2006—Age 15-19 spend one hour per day
on average on computer/video games
 Government sponsored survey in South Korean—2.4% of the 9-39
population are addicted to internet (BusinessWeek)

Little experimental evidence in the field of economics on utilization
of self-control devices

Psychiatric experiments on alcoholics
 Psychology studies on game addiction

Online game provides a unique platform to administer and monitor
experiment to large number of subjects in a natural setting, at low
cost
Our Project

Field experiment utilizes a multiplayer online game
platform

Offers actual players different commitment devices

Use of commitment devices suggests existence of self-control
problems

Two types of devices in which present-bias players and cuesensitive players would utilize in different ways.
Model

A stylized discrete time model


Combine features of Quasi-Hyperbolic Discounting (Laibson
1997) and cue theory (Bernheim and Rengel 2004)
Timeline
Period 0
Period 1
Period 2
Period 3
Period 4
Computer
On/Off
Play or Not
Play
Play or Not
Play
Play or Not
Play
Incur Delayed
Cost
Model

Period 0

Turn Computer On


Computer Off


Allows subsequent playing in Period 1 to 3
No subsequent playing allowed.
Utility function
3
𝑈0 = 𝛽


𝜏=1
𝛿 𝜏−𝑡 𝑥𝜏 − 𝛿 4 𝐶
Time consistent regardless of β
Our measurement of welfare
Model

Period 1, 2 and 3

Play


Not Play


Instantaneous consumption x and incur delayed cost
no consumption, no cost
Utility function
3
𝑈𝑡 = 𝑥𝑡 + 𝛽
where
𝜏=𝑡+1
xτ is consumption from playing in Period τ
C is total cost of playing

𝛿 𝜏−𝑡 𝑥𝜏 − 𝛿 4−𝑡 𝐶
Time-inconsistent if β < 1
Model

x is random and take on two values
𝑥𝐻
𝑥=
𝑥𝐿

Realization of x observed by player before playing decision in Period 1


𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝜇
𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 1 − 𝜇
No incentive to play just to observe x
Increasing marginal cost
∆𝐶1 < ∆𝐶2 < ∆𝐶3
where Cτ is the total cost of playing in two periods.
Interpretation—delaying other activities is increasingly costly
Model

Cue-Triggered Mistakes

In each Period t, probability pt of entering a “hot” mode


play in Period t with certainty
Probability 1 - pt of staying in “cold” mode

Chooses optimally whether to play or not
 𝒑 = 𝑝1 , 𝑝2 , 𝑝3

“Hot” mode lasts for one period
 If assume instead “hot” mode lasts forever, lower incentive to
start playing and higher incentive to delay playing
Model

Allow misprediction in β and p

We assume that x, C and p satisfy

Period 0 self would want to play in two periods when x = xH.
Furthermore there is no time-inconsistency problem

Period 0 self would want to play in play in one period when x = xL,
but a time-inconsistency player will play for at least another
period

Positive chance of being cued in every period
Behavior Without Commitment
Device

To avoid self-control problem the player might
decide not to allow herself to play any games,
even if a positive amount of playing is desirable

The player allows herself to overplay when it
gives higher utility than not playing at all
Commitment Devices

Ex-ante Device X


At Period 0, the player can commit to blocking herself from
playing further once she has played a certain number of
games.
In-game Device I


At each period, the player can commit to blocking herself from
playing further after one additional game.
Cannot be initiated in a period where the player is in “hot”
mode
Commitment Devices

New timeline
Effects of Devices on Game Play
We expect treatment group to have

Fewer games per session

Weakly more sessions per time period

Effect on total number of games ambiguous
Prediction of the Model
Two questions,

How do self-control devices affect game play?

Would time-inconsistent players and cuesensitive players respond differently to different
devices?
Behavior with Commitment Devices

Time-consistent/β-naiveté, cue insensitive/p-naiveté


β-sophisticate, cue-insensitive/p-naiveté




Use nothing
Uses I in the period before overplay is expected
If only B is offered, always use it if the cost of overplaying is higher than
the expected consumption from overplaying
Use I only when offered both
p-sophisticate

Always uses X
 Random use of I if it is offered (never use if p = 1)
Crucial Assumptions

No habit formation between sessions

p and x are not affected by the availability of
devices

Block length is less than time between sessions
Pilot Experiment

Our attempt to the two questions mentioned



An online implementation of the board game Boggle


How do self-control devices affect game play?
Estimate the proportion of time-inconsistent players and cuesensitive players—not yet done
compete on finding the highest number of English vocabulary
words from a grid of letters within time limit
Approximately 10,000 regular players
Execution

Six treatments groups—100 subjects each

Each group consists of 50 “heavy” players and 50 “normal” players, “heavy”
being defined as playing over 10 games in each session on average.

One control group—600 subjects

Each treatment group received the device(s) in one of the six
possible orders







Group 1 – B, I, X
Group 2 – B, X, I
Group 3 – I, B, X
Group 4 – I, X, B
Group 5 – X, I, B
Group 6 – X, B, I
Each group received the same device(s) for one month at a time
Ex-Ante Device
In-game Device
In-game Device
Limit Reach
Some Statistics
Time Period Covered
Total Observations
-Collapsed to Player-Day
No. of Players
-In treatment
-In Control
Within Treatment
Days Played
Games Per Day
Sessions Per Day
Avg. Games Per Session
Avg. Correct Guess Ratio
Avg. Rank
Avg. Break Duration
(in days)
N
Pre-Treatment
4/8 - 6/7
Treatment
6/8-9/7
32879
49588
507
520
329
353
Used
21.43
(16.02)
16.75
(11.76)
1.90
(1.00)
9.66
(0.13)
0.65
(0.13)
0.44
(0.20)
6.22
(14.30)
No Use
9.81
(13.21)
13.68
(12.02)
1.71
(1.02)
8.28
(6.10)
0.66
(0.14)
0.33
(0.21)
7.98
(16.89)
Used
27.47
(23.86)
11.77
(7.54)
1.75
(0.93)
7.32
(4.47)
0.65
(0.13)
0.45
(0.20)
8.45
(17.68)
No Use
17.44
(22.98)
9.82
(9.54)
1.70
(1.20)
5.75
(4.21)
0.67
(0.15)
0.38
(0.23)
17.10
(24.51)
119
388
121
208
Take-up Rate

Take up Rate
 At least once:
 At least thrice:
129
50
(38.97%)
(15.11%)
swap 1
swap 2
swap 1
swap 2
Effect of Treatment
Effect of Treatment
Regressions


Fixed-Effect Regressions at player-day level
Instead of player dummies we use player-day-of-week dummies because
players mostly play in the same day every week.
Treat. Group x Treat. Period
Constant
Games Per
Day
Sessions
Per Day
Games Per
Session
-0.80
-0.05
-0.49
(0.42)
(0.05)
(0.18)
17.37 **
2.27
**
8.84
(0.24)
(0.03)
(0.11)
Month Dummies
Yes
Yes
Yes
Player-Day-of-Week Dummies
Yes
Yes
Yes
Player-Day-of-Week Clustering
Yes
Yes
Yes
F
24.30
0.66
38.56
N
27654
27654
26492
** Significant at 1%
* Significant at 5%
**
**
Regressions

Does the devices have effect on players who chose not to use the devices?
Games Per
Day
Used Device x Treat. Period
at least once
Treat. Group x Treat. Period
Constant
Sessions
Per Day
Games Per
Session
-0.01
-0.78
(0.66)
(0.08)
(0.28)
0.03
-0.04
-0.12
(0.48)
(0.06)
(0.20)
-1.73
**
17.38 **
2.27
**
8.84
(0.24)
(0.03)
(0.11)
Month Dummies
Yes
Yes
Yes
Player-Day-of-Week Dummies
Yes
Yes
Yes
Player-Day-of-Week Clustering
Yes
Yes
Yes
F
21.00
0.58
33.21
N
27654
27654
26492
** Significant at 1%
* Significant at 5%
**
**
Is the Block Binding?

Most subjects who used a device do not log back in right after the
block ends

Block duration: 60 min
 Average duration between sessions in treatment period




Mean:
Median:
1 percentile:
20910.88 min
5854.813 min
363.767 min
= 14.52 days
= 4.07 days
= 6.06 hours
What does it mean for those who do?
ID
Time when
Device Device was set Games Allowed
Time when
Forced to Log Off
Time when
Log In Possible
Again
0XG3
X
14:55:46
4
15:11:30
16:11:30
0XG3
X
16:39:02
4
16:56:30
17:56:30
0XG3
X
18:20:11
3
18:34:00
19:34:00
0XG3
X
19:48:32
4
20:04:00
21:04:00
0XG3
X
21:12:06
4
21:30:15
21:30:15
Regressions

Do different devices have different effects?
Games Per
Day
Both Device Available
In-game Device Available
Ex-ante Device Available
Constant
Month Dummies
Player-Day-of-Week Dummies
Player-Day-of-Week Clustering
F
N
** Significant at 1%
Sessions
Per Day
Games Per
Session
0.26
(0.49)
-1.70 **
(0.46)
-0.95 *
(0.47)
14.29 **
(0.44)
0.04
(0.06)
-0.11 *
(0.05)
-0.08
(0.06)
2.28 **
(0.07)
-0.29
(0.22)
-0.56 **
(0.20)
-0.61 **
(0.19)
7.18 **
(0.19)
Yes
Yes
Yes
21.83
27654
Yes
Yes
Yes
1.92
27654
Yes
Yes
Yes
29.59
26492
* Significant at 5%
Normal and Heavy Players

Regression coefficients cannot be applied to the population
directly because we oversampled heavy players


Heavy players had a higher up-take rate


Used once—49.38% versus 35.6%
There are also a lot fewer of them playing by the time of
the treatment period


Will be running weighted regressions later on
81/300 versus 250/300
Have not looked into whether there is a difference in the
effect of the devices yet
The Next Experiment

The loss in subjects throughout time was higher than we
anticipated. The next experiment would need to start
with a larger number of subjects

More flexible devices


n-more-game button?
Investigate if a simple reminder on the possibility of
overplay has any effect on game play
Further Research

Replicating the pilot on games that are commercial and more timeconsuming


Word of Warcraft or MSN messenger?
Proxy for cues with gaming environment?

A hard or an easy board
 Competing against good players

Investigate the effect self-control devices have on demand for games

Effect could go either way
 Administrating the devices to new players only in order to study such effects?

Whether self-control is a problem in working environments, and whether
self-control devices can mitigate that