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5000
4
4
4000
3
3
3000
1
2000
1
2
2
1000
4
2, 3, 4
3
1
2
1
0
QFP1
(sub.)
QFP1
(win)
AL1
(sub.)
AL1
(win)
AL2
(sub.)
AL2
(win)
a. One QFP vs. two ALs, Pattern 1
5000
4
4
4000
3
3000
3
1
2000
2
1
1000
4
3
2
1
2
0
QFP1
(sub.)
QFP1
(win)
AL1
(sub.)
AL1
(win)
AL2
(sub.)
AL2
(win)
b. One QFP vs. two ALs, Pattern 3
Fig. 1. Average submitted and winning integers for each ranked player in in ( N,M )=
(3 , 4) DIY-L with φ · =0 . 1and λ · = 100 . 0
medalist 6 . Now that the integers 1 and one of the larger integers are occupied,
the lowest ranked player has almost no chance to win, which makes her submit
one integer randomly. A possible reason why no runs belong to pattern 2 in
( N,M )=(3 , 4) with one QFP and two ALs is that the decision-making pro-
cess of QFP players is more costly (Figure 1b and 2b) 7 . On the other hand, in
6 Note that the silver medalist does not submit one of the integers except 1 with equal
probabilities. In other words, the 2nd prize agent keeps submitting one integer, 2, 3,
or 4.
7 This is true for the games with λ · =10 . 0, namely the reason why one of the adaptive
learners is the 1st ranked is that she learns to submit 1 relatively more often than
others.
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