Information Technology Reference
In-Depth Information
Here we consider a second approach based on user interaction with different game
design elements. We measure the utility of a game design element
g
for user
u
in
achieving task
T
by means of a utility function
f
U
:
U
×
G
ₒ R
,(
u
,
g
)
ₒ
s
ug
.
The utility-scores
s
ug
capture to which extent each user
u
together with design ele-
ment
g
contributes to some overall goal. Given a utility function
f
U
, we select a
classifier
f
∈
F
according to the rule
g
u
=
f
(
u
)
=
argmax
g
∈
G
f
U
(
u
,
g
).
Thus,
f
assigns user
u
a game design element
g
u
with maximum utility.
Table
9.8
provides an example of a utility function
f
U
showninmatrixform
S
. In this example, we would assign game design
g
3
to user
Ann
. For user
Bob
the maximum score of 5 is achieved for design elements
g
1
and
g
2
. In this case,
we can pick either
g
1
or
g
2
as design element for
Bob
.
In practice, however, the matrix
S
is sparse for various reasons. For example,
users might not be willing to explore all design elements and may quit using the
system. Table
9.9
provides an example for the case of a sparse matrix
S
of utility-
scores. In this scenario, we aim at learning
f
U
on the basis of
n
observations
(
=
(
s
ug
)
consisting of
n
users
u
i
together with
corresponding game design elements
g
i
and utilitiy-scores
s
i
.
The problem of gamification reduces to estimating a functional relationship
u
1
,
g
1
,
s
1
),...,(
u
n
,
g
n
,
s
n
)
∈
U
×
G
× R
f
:
U
×
G
ₒ R
,(
u
,
g
)
ₒˆ
s
ug
that
best
predicts the utility-score
s
ug
of design element
g
for user
u
by means of
f
s
ug
. To clarify what we mean by
best
, we introduce the notion of loss
function. A loss function
(
u
,
g
)
=ˆ
s
when the true
utility-score is
s
. A common choice for a loss function is the squared error loss
defined as
(
ˆ
s
,
s
)
measures the cost for predicting
ˆ
Table 9.8
Utility-scores for six users and seven game design elements
g1
g2
g3
g4
g5
g6
g7
Ann
0
2
5
3
1
4
4
Bob
5
5
3
3
4
1
0
Col
1
3
4
2
3
3
5
Don
5
4
2
4
3
3
2
Elk
5
5
4
4
3
0
1
Flo
2
1
4
4
3
5
4
Scores are values from
{
0
,
1
,...,
5
}
. Higher scores indicate higher utility and vice versa
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