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In-Depth Information
Tabl e 5.
Game patterns in (
N,M
)=(4
,
4) 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
32
23
25
20
0.1
1.0
96
4
0
0
0.1 10.0
100
0
0
0
0.1 100.0
100
0
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
21
23
17
16
13
10
0.1
1.0
83
16
0
1
0
0
0.1 10.0
0
8
10
41
26
15
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
16
20
26
38
0.1
1.0
0
1
10
89
0.1 10.0
100
0
0
0
0.1 100.0
100
0
0
0
exp(
λ
f
· E
i
(
t
)) takes a value close to unity. Second, for
λ
·
=1
.
0, AL player(s)
often became the loser(s). This implies that it it preferable for the players to have
more information to win the game at this stage. Third, as sensitivity parameter
λ
·
goes larger, the game patterns become different between three-player DIY-L
and four-player one. In four-player DIY-L, on the one hand, only one QFP (or
AL) player could successfully dominated the game meanwhile one AL players is
the 1st prize and the 4th and two QFP players share are the 2nd and the 3rd
when DIY-L is something like a doubles game. This is independent of
M
and
λ
·
.
On the other hand, in three-player DIY-L, there is no apparent characteristics.
It is true that AL player(s) have diculties in winning the game for
λ
·
=10
.
0,
but there is mixed evidence for
λ
·
= 100
.
0, namely AL players won in some runs
but not so in others.
Figures from 1 to 3 show what kind of integers each ranked player submitted
and, if she is a winner, then won. Here, we provide the following characteristic
results: (
N,M
)=(3
,
4) DIY-L with
φ
·
=0
.
1,
λ
·
= 100
.
0, and one QFP vs.
two ALs (Figure 1), (
N,M
)=(3
,
4) DIY-L with
φ
·
=0
.
1,
λ
·
= 100
.
0, and
two QFPs vs. one AL (Figure 2), and (
N,M
)=(4
,
3) DIY-L with
φ
·
=0
.
1,
λ
·
= 100
.
0 (Figure 1). In three-person DIY-L, a larger sensitivity parameter
does not lead to only one game pattern (Tables 2 and 3). What Figures 1 and 2
indicate that a player persistently submitting the smallest integer becomes the
1st prize and giving up choosing such an integer has possibilities to be the silver
