Information Technology Reference
In-Depth Information
Tabl e 4.
Game patterns in (
N,M
)=(4
,
3) lottery for the last 5,000 turns
a. One QFP vs. three ALs
φ
·
λ
·
Pattern 1 Pattern 2 Pattern 3 Pattern 4
0.1
0.1
29
21
21
29
0.1
1.0
64
23
10
3
0.1 10.0
92
7
0
1
0.1 100.0
96
4
0
0
b. Two QFPs vs. two ALs
φ
·
λ
·
Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern 5 Pattern 6
0.1
0.1
23
15
12
23
10
17
0.1
1.0
50
19
15
10
1
5
0.1 10.0
0
0
0
23
24
53
0.1 100.0
0
0
0
100
0
0
c.ThreeQFPsvs.oneAL
φ
·
λ
·
Pattern 1 Pattern 2 Pattern 3 Pattern 4
0.1
0.1
22
23
29
26
0.1
1.0
17
7
29
47
0.1 10.0
100
0
0
0
0.1 100.0
100
0
0
0
-
Three-person DIY-L (
N
=3)
Each game setup has the following three game patterns in accordance with
the ranking of QFP (or AL) player:
•
One QFP vs. two ALs
Pattern
x
(
x
=1
,
2
,
3) means that the QFP player is the
x
-th prize.
Two QFPs vs. one AL
Pattern
x
(
x
=1
,
2
,
3) means that the AL player is the
x
-th prize.
-
Four-person DIY-L (
N
=4)
There are six game patterns in case that the players are equally split into
two types while four patterns are considered otherwise:
•
•
One QFP vs. three ALs
Pattern
x
(
x
=1
,
2
,
3
,
4) means that the QFP player is the
x
-th prize.
•
TwoQFPsvs.twoALs
Pattern
x
means that the ranks of QFP agents are 1st and 2nd (
x
=1),
1st and 3rd (
x
= 2), 1st and 4th (
x
= 3), 2nd and 3rd (
x
=4),2ndand
4th (
x
= 5), and 3rd and 4th (
x
=6).
•
ThreeQFPsvs.oneAL
Pattern
x
(
x
=1
,
2
,
3
,
4) means that the AL player is the
x
-th prize.
Tables from 2 to 5 summarize how many simulation runs there are observed
in each game pattern for each game setup. The game patterns depend on both
the game setup and the learning parameters: First, the games with a smaller
λ
·
(= 0
.
1) shows a somewhat randomized behavior, but this is not surprising
because this comes from the fact that the logit functions exp(
λ
a
·
w
i,k
(
t
)) and
