The Neuroeconomics of Learning and Information Processing; Applying
Markov Decision Process
Chatterjee, Sidharta
Andhra University
14 February 2011
Online at https://mpra.ub.uni-muenchen.de/28993/
MPRA Paper No. 28993, posted 20 Feb 2011 20:23 UTC
!
!
!
! """"
# $
% & ' (
& ) *+,- .
/ 0 *1 ' +2**
0000
3 0 40
. 5 '
3 6 7
. '
4 0
7 0 0
7 ' 4
4 0 .
'
6 6 0 6 3
3 3 ' 3
.
8 3 )
8 38 3 ))
8 3 ) ' $ '
' 9 ' ' '
:& ) :& :& ))
:& ) *+' ;*' <,
( 0 )
( 0 )
( 0 )
( 0 ) (
" 6 . . 8 3 $ ' / &
.' & ' ( ' ' 3 ' 3 = 0
0 ' ' ' 0 . #. . 8
0 ' ( ' .
0 >
' 0! .
) *+,- .
.
*. *.
*. *.
? 0 0 3 3 0 '
0 3 3 0 ' 3 ' 3 =4
4444 . . $ @*<,1A
5 &$' 0
3 7 3
3 . 6 3
3 3 ' 6 7
3 6
. @ A 0 4
7 0 '
3
0 3 $
3 0 0
0 ' 0
. 3 ' 3 3 '
' $ 77 @+22,A' . . @+2**A' $ 77 @+22*A'
B $ @+2**A @*;;CA.
6 0
3 3 0
3 3 3 0 ' 3
6 7 3 . ' 0
' 6 3
6 ' 0 3 0 0 '
' 0 . ' 04
> 0 . 3
7 ' . .' 3 '
' >
6 7 =
0 0 .
0 4 '
3 6
0 0 . D
' 3 ' 0
6 40
3 ' 4
0 @B ' *;C1A 3 3 .
3 ' ' 7 6 7 0
0 40
3 ' 3
@% ' +22<A 40 > 0 .
3 ' 0 .
0
Δ ∑ E
D ' Δ > 0 '
' 3 ' ? =
0 ? =.
0 0 3 0 .
> 0 0
3 3 ' 0
0 > > 0 .
4 3
7 ' 6 0 3
0 0 0
0 0 ! .
0 3
3 3 3
0 0 0 ' 0 0
' 0 0 0 . 5 '
6 7
0 . ' 7
0 ' 3 '
3 ' 0 0
0 0 ' 0 !
3
0 0 . F ' 0
3 6 3 3
' 0 ' ' 0
. 0 0
. '
' 6 0 ? > 0 =
> .
0 6 ' 3 '
' 3
6 . 0
6 7
0 6 3
' ' '
4 3 ' 3
4 4 .
0! 3 ' 0
0 ' 3 '
3 0
' 0 6 . 9
' 6
0 3 ' ' 0 3 '
>
' 3 ' > ' '
' 0 0
6 7 . '
3 7 0 0 0!
6 3 0 3
0 6 .
5 3 ' 0 0 3
3 ! ' 0 0 ' 4
4 . '
3 3
@
4 A. ' 3
0
0 3 . B ' '
4 0
0 6 @
6 A 3 3 ' 0
5 0 0 *;CG 3
7 3 0 @ A 7
0 3 0 7 .
0 > ' 0 > '
3 ' 3 3 ' 3 0 H
5 ' 0 ! . 5 3 '
3 3 0
. $ > ' '
0 0
7 . 5 3 ' 6
6 . ' '
0 0 3 3
0 0 . ( ' 0
3 0
3 > 0 .
6 6 .
' '
0!
3 0 3 0
' 3 6 3 '
3 0
> 0 = 0 3
0 0 .
3
6 3 0 0 4 0
6
@ A. 6 6
6
3 0 3 3
. 0 ' 6
3
3 . $ 6
?3 0 = 3
6 3 3 6 0
@ 3 A. &
' 3 '
3 3 .
0 3 3 0 0
6 E . 3
.
> ' 3 ? = 0 7
0 3 0 7 ? 3 =
0 0 3 ' 3
. 5 '
3 0
3 ' 0 ' 0 4
@ ' *;;C' $ 77 ' +221A' '
' 0 6 ' 3 '
@9
' *;<GA. ' '
' !
0 0
3 3 0 3 0
6 4 3
6 . 5 3 '
0
. 0 3
0 4 3
' ' 4
. 6 0 '
0
0 6 0
0 3 3 '
7 0
. 6 ' 3
0 3 3 ' 3
'
' 3 04 '
3 3 3
0 .
. B . B
. B . B $ $ $ $ 3 3 3 3
6
@ ' '
' .A 0 .
& 0 0
3 0 0! .
3 0
0 ' > 0 >
0 3 ' 3 ' >
0 . '
= 0
> 0 3
3 '
> 0 .
@/ ' *;I,A 4
0 0 3 3
' 0 0 @ ' *;C<A.
' 3
0 =
6
3 ' 3 ' 0 '
. ' 0
4 6 '
' . '
0 3 0 '
6 . 0 3 0
' 3 ' 7
.
3 0 4 7
3 3 . D '
0 0 .
6 3
'
3
3 ' 6 6 3 '
3 . B '
3 3
. 5
0 6
6 0 3 ' '
'
6 0
.
0 3 3
7 > 0
3
6 > 0 ' 3
7 7 @ ' *<GC4GC'
*<;2A. ( ' 3
6 3 0 3
0 6 @ '
*;;CA. > ' 3 3
0 0 J &( 3 0
7 4 0 0 @*;I,A
4 0 3 6.
3 = 6
J 0 0
0 0 J % '
= J D 0
' .
3 = 6 3 6 .
' ' > 0 0 @ =
0 0 A 3 '
0 0 6 = 0 @ '
*;;CA. ' 3 3 4
0! &6 ( @ &( A '
' 4
@# A. 5 3 ' 3 >
@ A 3 =
3 ' =
3 =
. ? &> 0 ='
3
. 3 3 3 . .' 3
= 3 0 3 = 3 .
0
3 4 0 ! @
0 3 0 6'
0 A. ' 3 '
!
7 @ 7 A
0 ! 0 0 0 0
' 3 6 ' .
5 3 ' 3 ! 0 ' 0
' ' = 3 3
3 ' ' 3
0 .
0 7 4
0 8 @*;C;A
. ' 0
0 0 3 3 .
' 3 ' 0
0 ' 3 ' 0 '
. '
6 ' ' 0
3 0 3 3
0 0 0 0 .
' 3
3 4 ' 0 ' @*;I2A' 5
@*;I+A' ' B @*;IGA' @*;I,A' 8 '
' ' 5 0 ' 3
> 0
0 .
> 0 > 0 ' ' 3
> 0 ' 3 J
7 3 0
7 ' >
. 0
0 .
0
0 7
0 . 5 3 ' 7
3 3 3
3 @ . .
+222A. / 6 '
0 4 3
' 7 6 7 3
3 '
3 . 5 '
7 0 0 3
3 6 0
3 0 ' 6 0
. 6 3
= 0 4
. @B
$ ' +2**' B B 3 ' +2*2' 5 . . +221A'
0 0 3 6 0
6 0 ' 0 3 '
0 . 0 3
0 '
3 0 0 @8 '
*;C;A' 0 ' '
?B $ =4
5 0 = 0 . B
0 0 ' . .'
3 ! 3 0 7
3 6 3 . 3 3 0
0 3
= 0 ' =
.
0 3 3 '
@*;I2A 0
3 3 . 5 3 '
0 ' > 6
0 3 '
0 0! '
' ' '
. 5 = @*;I+A 0!
0 7 0!
3 ' 3 .
0 3 *
@$ 77 +22,A 3 0
0 0 . '
> 3 > 0 0
.
0 .
.... % % % % $ $ $ $
% 6 ' 0 3
0 6 . F '
0 6 3
7 4 .
. '
0
6 0 0
0 !
3 . 5 ' 6
*$ & & 3 0 $ 77 ' & @+22,' +221' +22GA
.
0 ! . '
3
. 3 ' 0
0 3 6
6 ' ' 0 0
04 6 0 3
0 . $ ' 0 0
6 3 0
3 . 6
0 CEIK*+ ' CE K*+ 0 3 . D '
E0K 3 ' KC' 0KI' K*+. 5 ' 0 0
.+ 5 3 ' ? =
' 0 3 > 7
3 ? =. 5 '
0 ' ' ? =' .
> 0 0 3 . & ' ? =
?0=' 0 6 . .'
C ' 3 I 0.
0 6 3
' 3 0 6 3
0 0
2 To be noted, is and nothing else as well as for and the gives nothing but as stated product of the effects of . From this representation, it seems that the law of this equation is bounded which is rational for which, there may be a fixed number of contexts to define either ‘ ’ or ‘ ’ while, the ‘ ’ remains unchanged. Herein, if we assign the concept of cause as unknown= , a requirement 7 12 to discover outside the concept of ‘ ’ a predicate ‘ ’ foreign to this concept (related to the concept as cause of ‘ ’) is sought for, and solving for x gives 5. Now, a different representation of the context as given by 7+ ( 1 12 or 7 4 12 must be as a subproduct of the representation b=5 and nothing else so as 7 5 12. However, similarly, the cause may by represented as well by ( 1 5 12 !" 1 5 12 wherein, the product of 1 !" 1 must be, 7. While, a causality of 7 # 12 gives # 5. Now by substituting 7 # 5 12 yields the value for – # 0 and the rationality of 7 12 is established. Similarly, 7 & '() 12 would require more methodic iterations to establish the empirical universality of ‘b=5’. Thus, the rules remain the same but the iterations and subrmethods may alter to attain the same goal. This is a simple example of multiple representational states of a single causality.
3 . 0 3 3 3
0 3 0 > .
5 ' 6 6 7
3 3 6 @B ' +22<A ?
! 3
! 0
=. 3
? =' 3 ' '
.
#
# #
#....
.... $$$$
% >
0
' . .' 0 ' ' '
' ' 0 ' .
' 0
3 0! ! 4
? =. ' L
3 0 0 3 6 0
0 M.
0 > 0
3 6 >
. B 3 3
' 3 !
' 0 3 .
N O
*.
4 3 0
0
6 @
A. D 6 3 ?9 =
0 .
0
3 3 3 ' 3 0
.
4 0 3 6 0 3
3 '
3 0 6
0 .
Human Cognition
Human Learning Behavioral Neuroscience
Computational/ANN/
Robotics/ AI
Cognitive Ethology
Natural Intelligence
Animal Behavior
Animal Learning Animal Intelligence
Cognitive Neuroscience Cognitive
Economics
Neuroeconomics
Machine Learning/
Control Theory
.... $$$$ 44440000
$ 0
6 7 3
3 ' = 3
. 0 .
B 3 0 . 5 3 '
' ' 3
3 '
$. . ' ' 0
. 7
. B '
. '
0 . 5 3 ' : 5 = ?9
= 0 3 ' 5 =
@*;<GA
. 6 0
@*;**A 0 4 4
3 & 3
. $ 5 @*;G2A
@ A' B 3
0 .
$. . ' 3 '
. 0
. / 3 ' 0 3 7 3
6 3 .
6 $. . 0
3 0 3 .
= @*;;IA , 3 0
* *
*
*
+ 4I22 +2
/ ' ' 3 0
*. ? = K*+,, + … . +/0
+. ? = K* ,, … . 10
,. $ 3 $) P P →ℜ
,
*. 2 →* →,→I +. 2 →* →1→I ,. 2 →+ →1→I
3' 0 ' 3 0 0
*. 2 →* →,→I K * E * E * K , +. 2 →* →1→I K * E * E +2 K ++
,. 2 →+ →1→I K + QI22 E +2 K 41C<
6 0 3
3 6 3 @ 6
0 A. 0 3 4 3 3
3 ' 0 4 4 . /
6 ' 3
3 3 ' 0 6 6 ,C 3
.
1 3
0
2
5 4
A
A
B
A A
B
A
,$ $ 0 B ' +22I )
)RR333. .3 . RS3 R
/ .* 9 $ 3 ' ' $ 3 /
0 4 3 '
0 0 . >
! 0 3 4 4
0 0
6 3 . 6 $. .'
?2= K*S1 S2. . . Sn0.
3 3 ' 3 0
@0 4 A. 0 6 0
3 0 3 3 0 ' 0
6 ' 6 . 0 @
6A 0 0
3 0 . 0
0 3 ! .
*1 ++ 0 @ 0 A.
& 3 ' 0 > ' 0
3 4 4 '
0
7
10 4
1
9
2
5
14 11
8 12 6
3
13
8 3
1 5
1
5 2
1
6 1
1
12 >100
40
10
>20
15
>10
1
>5
100
6
2 S
A
0 0
6 7 3 ' 3
. 0 3 0 '
@ A
3 ' 0 3
. 3
0 ++ 6
3 0 . .' ' 0'
' ' 0 ' . 3
5 ∑ 56, ,, … ,/
<I' 3 ' T . / 3 '
6 7 3 ' *2,' **+
**1 . @ A 0
3
3 . 0 7 )
*. @ *E +AK*+EC1K<G
+. @0*E0+E0,AK4,GEIEGCK,G ,. @ *E +E ,AKCI41E*,K<1 1. @ *E +E ,AK4*+E,EGIKIG I. @ *E +E ,AK4,E*,ECGK<G'
G. @ *E +E ,AK**+E*2,E**1K,+;
$ 3 # 0 @ A) <;+ @ ;G.<IUA
6
Ρ K 8, 8 … / @*A
' '
9: 8, 8 … / ,
@+A
3' 0 0
0 0 3
; cos sin @ KA @,A
D ' Ρ 8, 8 … /
@,A G.2CGI' G.22<+' G.1C<1'
C.C,,+' G.2CGI C.CG . 3 >
7 . >
'
sin ∑ ∑6, ,6 5 @1A
D '5 g1 g2 g3' 0 .
B 0 @+A @1A' 3 ' 8, 8 … /
'
9,: 8, 8 8D 8E 8F 8G sin ∑ ∑6, ,6 5
@IA
6 3 ' 6
0 0 . ( 4
' 0 0 ' '
= 6 .
> 3 ' 0 0
V 0 '
Hƒ + J;KL M@ @I.*A
0 0 .
6 ' 3
0 0 .
' ? = 40 3
3 ' 0 ? = 0
. 0
0 / @*;C2A
. (
' ? =' @VA.
0
ƒ N HL, *O + 0PQRST U N HL,*V + 0
> 0 '
WX* |Z|0 W* ;Z 1@
Z 1
> @*1A'
> 0 V 9[\,[RS .
0 0 '
6 0 7 ' 0
40
3 0 0
' 9[\,[RS ' 9[RRS]S ^_
[LRS]S \[ . 3
7 0 0 0 0 .
7 > '
5 sin `ab c/ c\c @GA
D ' 9: 8, 8 … /
, ' ' ∑ ∑6, ,6 5
. B 0 0 @GA'
> '
d 8, 8 … /
:
,
sin e e 5
,6 6,
sin ∑ ∑6, ,6 5
Psin ∑ ∑6, ,6 5 sin ∑ ∑6, ,6 5T 7
D ' 9,: 8,
8 … / > @+A. 3' 0 @GA ' 0
5
`ab c\ f\, @<A0 0 @<A' '
2 g sinP∑ ∑6, ,6 5T 2 h9,: 8, 8 … / h
2 1
@;.*A
2 g sin ie e 5
,6 6,
j 2 kd 8, 8 … /
:
,
k 1
@;.+A
/ > @;A' 3 3
0 11.GG '
1*. 9 0 > @;.+A'
0 0 3 0 0 0 0 3
3 4 0
0 ' 3 <<.,,U
' *+U 4 . 0 '
3 @ 0 *A' 3 @
UA 0 3 3 3 ;G.<IU.
D ' 7
0 ' 0 6 0
> @GA
5 sin 2 1 @*2A
D '
+lm ie e 5
,6 6,
j 2 kd 8, 8 … /
:
,
k 1
@**A
B > @**A' 3 C<.+<U C+*.+,' 3
> @CA GCG.+,' 3 0 0
' 3 0 ' 0 @*2A' 3
5 +lm ie e 5
,6 6,
j kd 8, 8 … /
:
,
k
kd 8, 8 … /
:
,
k 1
@*+A
6 3 7
6 0
@3 0 3 A *,I,.,; @*+A' 3
@**A' 3 C+*.,, 3 . 3' 3
++ ;+*. ' 6 0
3 3 3 0 0 3 0
' #KC+*E;+*K*G1+' 3 ' 6 '
6 7 3 ! .
0
> 0 0 0 '
3 ' 0 0 3 0 7
. 0 0
' 3 ' 6 0
3
' '
0 .
> 0 0 . '
0 @;.+A '
6 ' ∏ 56, 7 '
oK
p,\q∏tsuSrs\∏ vs^w∏ vs
tsuS x tsuS
∏t vs suS
yz
{
∏tsuSrs
@*,A
D ' o 7
7 0 @ / '
7 > )
2 g +lmP∑ 56, ∑ 56, T ∑ 56, g & 2 g h9[\,[RS 8, 8 … / h) q1 |∏ 56, ∏ 5 P∏ 56, 6, T
∏ 56, }y
∏ 56,
~/
@*1A D ' & 2 g h9[\,[RS 8, 8 … / h) 0
• 2 g k9[RRS]S ^_
[LRS]S \[ k 8, 8 … / €.
% '
2 g +lm ie 5
6,
e 5
6,
j e 5
6,
g
• 2 g k9[RRS]S ^_
[LL,:
, \[
k 8, 8 … / €
∏ 56, ~/
@*IA
+< 3 / 87 ' / 50' 3
7 *G' 3 ' 3 6
. 7 0 3 ' 9 [[^SRS . >
@*1A 3 > @<A' 3 7
> @9%#&A 3
0 0 0 3
' ' 3 ' '
0 . 5 ' ?~/=
7 0 = >
. / > @*IA' 0
7 . > 3
3 6
J
0 0 0
3 3 J
0
' 0 3 0 =
$ J
> ) $. . 0
0 ' 3 0
J
' 0
0 0 7
0 ' 0 3 3
3 0 3
3 . ' 3 >
@ ' +22;A .
5 ' > 0
3 '
' '
. '
3 3
' 3 0 3 3 0
7 3 0 3
' 3 0 ' 7 '
0
@ A . 3 0 ' 0 3
@ A @ A 3
3 7 .
!
0 @ ' +222A. 3 0
0
3 0 3 @ A 3 3 '
0 0 '
! ' 3 '
3 0
0 @/ ' *;;C' ' *;;;A'
3 3 ' 3 .
B 3 > 3 3 3
' 0
3' 0 0 ' . .' 3
' 6 '
3 0 0 0
3 6 7 3 .
3 0 7 0 *@ 6A.
3 ' 0 3
0 . '
0 6 7 3 3
3 3 3 .
0 3
$ @ A.
6 7 ' 3 '
6 7 3 0 .
5 3 ' !
0 0 3 '
' 0 3
. 0 0 3
3 0
3 3 ' '
6 ' 3 . 5 '
6
' @ '
/ ' *;I1A. 0
6 6
@ . . +22CA 3 ' 0
3 4 4
3 . 04
.
' 0 0 0
3 @ A. 5 3
0 @ A 3
! 3 6 0 . 5 3 '
> 3
? = > 0
3 3 > 6 0 3 .
#.
#.
#.
#.
0 0
' ' 3
0 ++ . 5 3 ' *I
0 ,C @
A. > = 0 0 0
4 0 0 6 = 0 3
0 3 ' 3 ' 4 ' 6 ' 0
6 ' 0 . D 0 6
0 ' 0
0 0 3
3 0 . 7 0
0
0 0 7 0
3 ' 0
3 6 0 . 7
0 3 ' '
3 6
. 3
0 6 0
6 .
0 3 3 @*;<*A 3
0
0 . '
=
3 ' ' '
> . 6 '
>
6 . 4
6 3
. ' > 0
. 0 0 '
. 4 ' 3
0 > .
'
4 4 3 ' .
6 > 6 0
0
> .
E
%
/ .+ 0 4& 4
$ @*<,1A'
0 3 0
3 > 4 ? 0 0 3
Agents Given Tasks
Ability Effort
Success Failure
Motivation
3 0 ' 0 3 3 0 ' 3 ' 3 =.
0 3 3 0
3
0 3 0 '
6 ' 6 . 3
0 0 3 3
0 3 0 '
3 3 ' 3
0 3 4 '
0 . 0 ' 0
0 0
0
$ > 0 3 4 .
$ 3 0
6 '
6 @ ' +22;A 3 4 '
6 . 0 =
' 4 4 4 0
$. . 0 = 3 7 '
4 . / '
0 0 0 3 3 >
0 0 3 > .
/ 6
0 7 3 0
0 3 3 0
0 . 0 6
3 0 @B . .' +22<A
0 = 7 =
0 4 0 0
' ' 0 6 3
4 0
0 3 .
0000 ))))
8 3 0 3 0 3 6
0 3
' 0 . 5 ' 3
0! '
3 3 ' 0 ' 3 ! 3
. 0 6
*22 0 3 *22 . % '
0 I2'222 0 3 +24CI'
7 0 0 *2U 0 CI.
6 3
.
0 3
$
0 .
0 3 ' '
' 3 .
3 3 6 '
3 3 ' 0
6 0 3 . 6
0 0 . %
0 '
3
> 0 .
5 0 6
' 0 .
0 3
0 7
. 5
3 0 ' 0 '
3 0 6 .
3 0 6'
' > ' '
3 0 '
3 0 .
4 0
> ' 6' @9 ' *;;;A'
3
' 7
@/ . .' +221A' = 9 ' '
0
. 0 0
3
' 0 3
. . 0 @*;;+A 3 4
6 0 4 > 4B
@ 40 A 6
3 3
0 0 3
7 = . = '
0 4 0
0 3
= @ 7 ' *;;<A. (
' 3 0 7
3 0 ' 7 0 0
0 0 .
5 0
0 0 3
0 6
0 . 0
3 0 .
0 ' 0 0 0
;)*. 5 3 ' ' 0
‚ G„ e …a‹ b S‡ bb O` Š
/6, , @*IA
3
0 .
0 3 6 0 B 8 @*;C<A
0 3 .
' 0
' 0 3
' ' . 5 3 '
0
' 3 ' 0
3 4 . >
3 ' 0
J D 0 0
0 J
B.
B.
B.
B. $$$$ 9999
% > ' 3
VŒ 0 J 0
.
0 4 .
0
0 . 9 3
3 .
0 0
. 0 ' 0
0 ;)*. ' 3 0
3 0 0
' 0 0 . B
0 > 3
3 ' 0 . &
@ '
' ' I45 .A . & 3
6
3
@ *;;2' 8 *;;GA. 4
6 . 5 3 ' @ A
. 9
0 3
3 .
0 3 .
0 3
'
3 0 . 3 0
0
0 3 0 3
' 4
> . 0 0 0 @
. . +22+A @ 0 3 A
3 3
. ' 0 0 7
0 3 0 3
. ' 0
0 0
. ' 0
> 0
3 @ 3 A >
. 0
7 3
3 0 >
3 @ 4 6 A 3 6
0 0 ! .
' 6' ' ' * '
' 0 3
. ' 3 3 0
J 3
3 0 0 ' ' . .
0
. ' 4
' 3 '
0 0
3 3 0 3 0 .
' 0
3 W B 5 @8 ! ' +2*2A
@
JA 3 ' 0
.
L M
3 0
4 .
# #
# # . . . .
0 3
' 3 40
0 0 .
4 0
4 3 .
0 0 0
3 0 3
0 3 '
. 0 6
3
3 0 . %
' '
' 0 ' L M 0
0! .
$ )
$ )
$ )
$ )
' . @*;I2A ?( ' & & =' :
& ' . I<) +**4++*.
' . @*;I+A' L X > ) >
XY Y M' & ' +*' . I2,41G.
' D. B . @+22IA. 5 0 & '
# . +) 4B & ' 8. : . ' '
& &# &$R 45 .
' D. B .' ' ' ' . @*;;CA. &
& 6 . .
' :.D. @*;ICA. ? 4 0 =.
$ 3' G1 ,I;4,C+.
B ' 4 $ ' $ ' . @+2**A. 0 0
4 .( ' ' D
. **R*G.
B .5.' .' ' . ' :. @+22<A. B
= ' % B
: ' +22<' +' *4*+.
B ' .:.' ' .@*;C1A % .
$ 3' <*' I2G4I+2.
B ' .' 8 ' 7 .@*;C<A. 0 . . $ .
.*),I@I;A.
B ' ' B 3 :. @+2*2A )
% B ' / . $ . B B D . *24*G.
B . +22<. ) '
' ' 0 ( .
5. : ' / &. ' 0 . ' :$) *;;,.
) ) . . . . ( # .
;2' . I;I;4I;G,' : *;;,' B .
.:. / . @*;C2A. B =.
0 ' . ,' *4+G.
. @*;;CA 4 W 5 & ) %
B WD&$ F. &
5 . %6 ) ( %6 .
' 9.' / ' .' ' .' ' . @+2**A.
7 . 4 4 . 0
' = ' ' D '
+2**R21.
& @+22+A' ZB % 7 B Z' :.:. @ A'
& ' % 7 ) & $ .
' ' & 3 & .
/ ' . *;;C. # ) 3 ? = .
# ) ' / . ) .
/ ' $. .' 49 ' B. +22+. 3 4 '
)# . +;<' IIG4IG+.
/ ' . ' ! 3 ' W. : ' ' 4F # ' +221.
) 3 0 4 .
' # . *2' *2II4*2G,.
/ . @*;I,A' & & ' ( ' .
5 ' . .' $.&. / @*;IGA' L M' . B
. $ @ .A' 9 ) # . 0 ) (
.
5 ' /. . @*;I+A. % . > /
' ) $ [ 8 .
5 ' /. @*;11A. . $ 3'
I*) ,I<4,C,.
5 :.5.' 8. 5 . @*;<GA' $. 0 ' . ' ' .
5 ' ' 8 ' ' 0 8 @+221A B
0 ) 6 0
. & ) # . C+' C<*4<++.
8 ' ' . @*;C;A. )
. & ' # .1C' . +' +G,4+;+.
8 ! \ %. $ )@+2*2A ( & B '
W B 5 ' 8
> 7 X . / . +2*2 *) *I. )
,22<;+G
.&.' 7 ' . . *;;<. = ' * +. 3 & : ' # .,,;' *2114*2I, **,24**1,.
. . . . D ' *;;1.
' : . +222. .
+;)I2C4I1<
' .' 9. ' . 7 . > @+222A' L 0 4
8 3 % 7 M'
' ;' CIC4C<<.
' . @*<GC4<A' F ' $ @*;;1A.
' . @*<;2A' & ' ) .
' &6 ( 5 0 & @:.
' D. 5 ' (. ' . ' & 3 & ' *;;C' . ,1+4,I2A.
' ' . +G +22C. )
' 0 6 & ' ( ]
) $ .,21;.
' ' $ 77 ' . @+221A B 3
& &6 & ) / 3 $ 5 '
. . & L . '
=& Z Z @ & & AD
. 2G.
' . 0 ' 0 J &&$ $
*+R+22;
% ff ' )@+22<A 0 8 4
0 40 . .
$ 77 ' ' & ' . @+22,A. & ) /
5 & . & L . '
=& Z Z @ & & A
D . 21.
$ 77 ' . @+22,A. 3 .
& L . '
=& Z Z @ & & A D . 2,.
$ 77 ' . +221. 8 3 4 ' :
B ' G' +II Q +C1.
$ ' . . @*<,1A4L 0 3
'M + .' ' .
. 5 0 . @*;C<A. $ 4 0 7 . 0
' < 0 ' *;C<. 4 ( ' 0 '
' ( .
. 5 0 @+222A' B $ )
3' [ ' # *' . *' +I412
' . 5 0 @*;CGA. L/ 0 $ M' ) .
@ .A & . 0 ) 0 ( .
.*+;4*1<.
' . 5 0 . @*;;;A. 3 . $ XY
. # . <<. + *;;;. . +,4,;.
' B.' .' 5 ' . .' 9 #.' / ' $. . +22+. ) 4
. '
# . ,G' .I' <II4<G<.
: 4F ' % 7 9 ' 9 . $ ' 5 9. . +221.
. 9 B ' # .*' ,4**.
' & 3 @*;**A' ) &6 ' 3 F '
.
6666
$ 3 / )
*. 2→*→C→;→**→*1 +. 2→G→<→1,→*+→*2→*1 ,. 2→1→I→*1
1. 2→*→1→I→*1 I. 2→G→1→I→*1
G. 2→G→<→+→,→*+→*2→*1 C. 2→G→<→+→I→*1
8. 2→G→<→*,→,→*1
;. 2→G→1→C→;→**→*1
*2. 2→1→C→;→**→*1
**. 2→G→<→+→,→*1
*+. 2→*→1→C→;→**→*1
*,. 2→G→<→*,→,→*+→*2→*1
*1. 2→1→+→,→*1
*I. 2→1→+→I→*1
*G. 2→1→+→,→*+→*2→*1
*C. 2→*→1→+→I→*1
*<. 2→*→1→+→,→*1
*;. 2→*→1→+→,→*+→*2→*1 +2. 2→G→1→+→I→*1
+*. 2→G→1→+→,→*1
++. 2→G→1→+→,→*+→*2→*1
0 *. # / 0
! 3 0 )
*. 2→*→C→;→**→*1K*E,E*EIE*K**
+. 2→G→<→1,→*+→*2→*1K*E*E*+4*22E12E*2K4,G@0*A ,. 2→1→I→*1KIE+E<K*I
1. 2→*→1→I→*1 K*4IE+E<KG@ A I. 2→G→1→I→*1K*EGE+E<K*C
G. 2→G→<→+→,→*+→*2→*1K*E*EGE*IE+E12E*2KCI@ *A C. 2→G→<→+→I→*1K*E*EG4+2E<K41 @ +A
8. 2→G→<→*,→,→*1K*E*E*+E*4*2KI@0+A
;. 2→G→1→C→;→**→*1K*EGE*22E*EIE*K**1
*2. 2→1→C→;→**→*1KIE*22E*EIE*K**+
**. 2→G→<→+→,→*1K*E*EGE*I4*2K*,@ ,A
*+. 2→*→1→C→;→**→*1K*4IE*22E*EIE*K*2,@ *A
*,. 2→G→<→*,→,→*+→*2→*1K*E*E*+E*E+E12E*2KGC@0,A
*1. 2→1→+→,→*1KIE+E*I4*2K *+@ *A
*I. 2→1→+→I→*1KIE+4+2E<K4I
*G. 2→1→+→,→*+→*2→*1K IE+E*IE+E12E*2KC1@ +A
*C. 2→*→1→+→I→*1K*4IE+4+2E<K4*+@*A
*<. 2→*→1→+→,→*1K*4IE+E*I4*2K,@ +A
*;. 2→*→1→+→,→*+→*2→*1K*4IE+E*IE+E12E*2KGI@,A +2. 2→G→1→+→I→*1K*EGE+4+2E<K4,@*A
+*. 2→G→1→+→,→*1K*EGE+E*I4*2K*,@+A
++. 2→G→1→+→,→*+→*2→*1K*EGE+E*IE+E12E*2KCG@,A
6 B 6.* % &
Total Initial Value of the system before the program: 85
Total value unlocked or rewards derived by the agents: 921
Total No. of Policies: 22
Mean (avg.) Reward per agent: 41.86
Efficiency Rate: 49%
Reward gained by following PP’s: (excluding. Top 3) 563
Reward Value of Top three Policies: 35.72 (329)
Reward Value of Top three Policies as a %: 35.72%
Reward Value gained by top 14 patterns per agent: 40.21
Efficiency of patterned policy choices: 61.12%
Mean reward gained by following random policies: 6.25
Total rewards gained following non-patterned policies as a percentage: 4.3%
Total Reward Value gained by following PP’s as a %: 96.85
6 0 6 +. 3
3 04 $ .)
*. $ $ )RR3334 3. . . R
+. ( 0 $
) )RR3 0 . . 0 . RS R0 R 0 R *.
FIELD N MEAN STD SEM MIN MAX SUM (Policy Groups)
A (a1+a2) 2 43.00 43.84 31.00 12 74 86 B (b1+b2+b3) 3 12.00 51.86 29.94 -36 67 36 D (d1+d2+d3) 3 28.00 41.58 24.01 -4 75 84 E (e1+e2+e3) 3 18.67 40.82 23.57 -12 65 56 F (f1+f2+f3) 3 28.67 41.77 24.11 -3 76 86 G (g1+g2+g3) 3 109.50 6.36 4.50 103 114 329