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pez{a
1.8
noliear
1.6
twopar
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1.4
block
1.2
pure
linear
AveragCumltiPof
1
0.8
0.6
0.4
1
10
100
1000
10000
Iteraions
1.2
noliear
’
block
twopar
1
pure
mixed
linear
0.8
’
’
’
’
’
AveragCumltiPof
0.6
0.4
0.2
0
1
10
100
1000
10000
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20
15
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10
Price
5
5
10
15
20
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70
60
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30
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1
N=100distrbuonfpmawxel
Distrbuonfpmawdxelgc
2. 2
g
2
twoparif
twoparif
mixedbunlg
mixedbunlg
2
1. 8
1. 8
1. 6
1. 6
1. 4
lognumberfsap
1. 4
1. 2
Lognumberfpitsacdwh
1. 2
1
1
0. 8
0
10
20
30
40
50
60
70
80
90
0. 8
100
0
10
20
30
40
RankOrdeofptim
50
60
70
80
90
100
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2
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1
1
twoparif
twoparif
0. 9
mixedbunlg
mixedbunlg
0. 8
0. 8
0. 6
0. 7
n
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0. 6
0. 4
0. 5
Autocrelai
Autocrelai
0. 2
0. 4
0. 3
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0. 2
0. 1
0. 4
0
5
10
15
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WindowSze
WindowSze
Autocrelainfdmwkspxbg(N=10,C=100)
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twoparif
mixedbunlg
0. 8
0. 8
0. 6
0. 7
n
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0. 6
0. 4
0. 5
Autocrelai
Autocrelai
0. 2
0. 4
0. 3
0
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twoparif
0. 2
mixedbunlg
0. 1
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WindowSze
Autocrelainfdmwkspxbg(N=100,C=10)
Autocrelainfpmzhswdxbg(C=10,N=100)
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twoparif
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mixedbunlg
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0. 8
0. 6
0. 7
n
n
0. 6
0. 4
0. 5
Autocrelai
Autocrelai
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0. 4
0. 3
0
twoparif
0. 2
mixedbunlg
0. 2
0. 1
0. 4
0
5
10
15
20
25
30
35
0
40
0
5
10
15
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WindowSze
WindowSze
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twoparif
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mixedbunlg
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0. 8
0. 6
0. 7
n
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0. 4
0. 5
Autocrelai
Autocrelai
0. 2
0. 4
0. 3
0
0. 2
twoparif
0. 2
mixedbunlg
0. 1
0. 4
0
5
10
15
20
25
30
35
40
0
0
5
10
15
20
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Model of 1. Get prediction
Opponent
of opponent’s
prices
3. Offer new schedule
2. Use amoeba
to select next
prices on 'virtual'
landscape.
sumer
4. Receive profit
3a. Actual Opponent
Prices
5. Update model given
profit and opponent’s
observed prices
Opponent
RBF network model
of profit landscape
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[<h j{hNe$ fNsxl{aN z<]_^9q<chL~]_[<a3^$f§sia3fgc`j<]_j<q<c`h~[<loadc c]iez+f§dsia3fgcadc ^`]iWj<fNsUhN2t cz<fge hNc n$hNca
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[o]w¢/adc`a3jHe j<]_%z{a3^d§9a c)]_s_scadel<c`j ebhVez<]x^)]_[<a3f ]_j z<fgq<ebadc,0~ cz{a3j ca [<]x^dl<^^ez{a$]_[{a3fphNt RWZS
6
+
λ=0.05
Comparisnflt,chedw.
900
800
700
monplisterac
600
nichebudlr
500
nichepratl
AveragCumltiPof
400
300
pricewa
200
(1)
pricewa(2)
100
0
0
20
40
60
80
100
Iteraio
120
140
160
180
200
180
200
]iWl<ca { { a3s_fge]iNa$qBadcthNc`npfNjoa hNtUfVn$hWj{hNqBhWs_]_^esia3fgc%j<]_j{Eq<c`]_a3^3emchkq<ch[<l<adc`^2c]iez¤ez{a
^`fNn$a qBadcb¥Jfgc`e]_dsiaL^``z{a3[<losiasia3fgc%j<]_j{qoc`]_a3^dgfNj<[|edch q<c`h~[<loadc`^Jc]_ez[<]w¢Badca3je^%z{a3[<l<s_a3^¦sia3fgc`j{¥
]xj{$q<c`]_a3^UthNcds_l<ebebadc)hW^behNt 0
n
λ=0.
Comparisnflt,chedw.
1
900
800
nichebudlr
700
600
monplisterac
500
AveragCumltiPof
400
nichepratl
300
pricewa(1)
pricewa
200
(2)
100
0
0
20
40
60
80
100
Iteraio
120
140
160
]iWl<ca {80~ a3s_fge]iNa$qBadcthNc`npfNjoa hNtUfVn$hWj{hNqBhWs_]_^esia3fgc%j<]_j{Eq<c`]_a3^3emchkq<ch[<l<adc`^2c]iez¤ez{a
^`fNn$a qBadcb¥Jfgc`e]_dsiaL^``z{a3[<losiasia3fgc%j<]_j{qoc`]_a3^dgfNj<[|edch q<c`h~[<loadc`^Jc]_ez[<]w¢Badca3je^%z{a3[<l<s_a3^¦sia3fgc`j{¥
]xj{$q<c`]_a3^UthNcds_l<ebebadc)hW^behNt /
6/
n
λ=0.
Comparisnflt,chedw.
3
900
800
monplisterac
700
nichebudlr
600
500
400
AveragCumltiPof
nichepratl
pricewa(1)
300
200
pricewa(2)
100
0
0
20
40
60
80
100
Iteraio
120
140
160
180
200
180
200
]iWl<ca {81~ a3s_fge]iNa$qBadcthNc`npfNjoa hNtUfVn$hWj{hNqBhWs_]_^esia3fgc%j<]_j{Eq<c`]_a3^3emchkq<ch[<l<adc`^2c]iez¤ez{a
^`fNn$a qBadcb¥Jfgc`e]_dsiaL^``z{a3[<losiasia3fgc%j<]_j{qoc`]_a3^dgfNj<[|edch q<c`h~[<loadc`^Jc]_ez[<]w¢Badca3je^%z{a3[<l<s_a3^¦sia3fgc`j{¥
]xj{$q<c`]_a3^UthNcds_l<ebebadc)hW^behNt n
λ=0.
Comparisnflt,chedw
5
900
800
monplisterac
700
nichepratl
600
500
AveragCumltiPof
400
300
pricewa(1)
200
pricewa(2)
100
nichebudlr
0
0
20
40
60
80
100
Iteraio
120
140
160
]iWl<ca { 6 a3s_fge]iNa$qBadcthNc`npfNjoa hNtUfVn$hWj{hNqBhWs_]_^esia3fgc%j<]_j{Eq<c`]_a3^3emchkq<ch[<l<adc`^2c]iez¤ez{a
^`fNn$a qBadcb¥Jfgc`e]_dsiaL^``z{a3[<losiasia3fgc%j<]_j{qoc`]_a3^dgfNj<[|edch q<c`h~[<loadc`^Jc]_ez[<]w¢Badca3je^%z{a3[<l<s_a3^¦sia3fgc`j{¥
]xj{$q<c`]_a3^#fN^)ds_l{ebebadchW^e)]_^Ugfgc`]ia3[VmBademcada3j 0 fNj<[ 80
6g
n
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]x^l<j<fgmos_aebh^l<^befN]_jVedc hEj<]_%z{a q<ch[<l<adc`^3
z<]_^U]_[<a3f9hNtXds_l{ebebadc)hW^bez<f ~]_j<fc%fNj{Na]_jc z<]x`zk]ie#dfNj n f+Nj a|j<]_`z<a thNc`n fge]ihWjkn$hNca|fgq{¥
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^`]iel<fge]ihWj]_^4cadNadc`^a3[fNj<[ ez{a ^ba3fgc%`z{adc j<]_%z{a]_^n9l<%zsxfgcNadc3HmBhNez q<ch[<l<adc`^4fgca^be]_s_smBadebebadc
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ezofNj ]ie]_^l<j<[{adc#qBadcta3e]_j{thNc`npfge]_hWj L j"ez<]_^#dfN^baNrez{a|mol<jo[<s_]_j{9q<ch[<l<adc^`z{hWl<s_[EmBa|fgmosia|ebh
6
Comparisnflt,chedw.|
|:c
1
|=4:1
2
Comparisnflt,chedw.|
300
|:c
1
|=3:
2
1
250
250
200
monplist
monplist
200
150
150
AveragCumltiPof
AveragCumltiPof
100
nichepratl
100
nichepratl
nichebudlr
nichebudlr
50
pricewa(1)
50
pricewa(1)
pricewa
0
0
20
40
60
80
100
Iteraio
120
pricewa
(2)
140
160
180
0
200
0
20
40
60
80
100
Iteraio
n
Comparisnflt,chedw.|
|:c
1
|=2:
2
1
120
140
160
180
200
180
200
180
200
n
Comparisnflt,chedw.|
160
(2)
1
|:c
|=1:
2
900
800
140
monplist
700
nichebudlr
120
600
100
monplisterac
500
400
AveragCumltiPof
Averagcumltipof
80
nichepratl
300
pricewa(1)
nichebudlr
60
pricewa(2)
200
nichepratl
40
100
(1)
pricewa
pricewa(2)
20
0
20
40
60
80
100
Iteraio
120
140
160
180
0
200
0
20
40
60
80
100
Iteraio
n
Comparisnflt,chedw.|
|:c
1
|=1:
2
:2
120
140
140
160
n
Comparisnflt,chedw.|
|:c
1
|=1:
2
3
200
180
120
nichebudlr
160
100
nichebudlr
140
120
80
monplist
monplist
100
60
pricewa
AveragCumltiPof
AveragCumltiPof
80
pricewa
(1)
(1)
60
40
pricewa(2)
pricewa(2)
40
20
nichepratl
nichepratl
0
0
20
40
60
80
20
100
Iteraio
120
140
160
180
0
200
0
20
40
60
80
100
Iteraio
120
140
160
i] Wl<ca {82~ a3s_fge]iNa$qBadcthNc`npfNjoa hNtUfVn$hWj{hNqBhWs_]_^esia3fgc%j<]_j{Eq<c`]_a3^3emchkq<ch[<l<adc`^2c]iez¤ez{a
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tchWn / ebh ~ /
n
6
n
150
niche
Per−article price
100
bundler
50
per−article
captures
entire
population
per−article pricer
0
0
50
100
150
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qBhW^]_e]iNa q<chgvoed
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Bundle price
60
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/d 1
Number of iterations to stabilize vs. number of congregators moving
10000
Iterations
1000
100
10
1
1
2
3
4
5
6
Number of congregators moving
7
8
9
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/d 2
Time needed to stabilize vs. number of labelers
10000
Iterations
1000
100
10
1
0
1
2
3
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30
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100
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NumberofItains
Computainlcsberfkd
400
350
300
250
Computaincs
200
150
100
50
0
1
10
100
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1~ : hW^be)hNt[{adebadc`np]_jo]_j{$ez{a9hNq<e]_npfNsyfNs_sihdfge]ihWjhNt4Nhh[<^fN^)ez<a9j~l<nmBadchNtnpfgcVjNade ¥
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Numberofaktplcs
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AveragNtPofipIn
300
250
200
m=
1
3
=m 5
m=10
m=25
m=50
m=100
m=250
m=500
150
m=
NetAvragPofi
100
50
0
-50
0
100
200
300
400
500
600
700
800
900
1000
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Iteraions
AveragPofits.NumberofMakts
300
250
200
150
AveragNtPofi
100
50
0
-50
1
10
100
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Numberofaktplcs
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Averagntpofis.umb
10
8
6
Averagntpofiduc
4
2
0
50
100
150
200
250
300
350
400
450
500
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300
280
Average Profit
260
240
220
200
threshold=r
threshold=0.75r
threshold=0.5r
threshold=0.25r
threshold=0.1r
180
160
1
10
100
1000
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/3 0
Average Profit per Iteration as Threshold is Varied
300
Average Profit
250
200
n=20
n=15
n=10
n=5
n=1
150
100
50
1
10
100
1000
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Model of 1. Get prediction
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2. Use amoeba
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sumer
4. Receive profit
3a. Actual Opponent
Prices
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profit and opponent’s
observed prices
Opponent
RBF network model
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