3-basic decision analysis
Post on 02-Jun-2018
219 Views
Preview:
TRANSCRIPT
-
8/11/2019 3-Basic Decision Analysis
1/33
Basic DecisionAnalysis
-
8/11/2019 3-Basic Decision Analysis
2/33
DECISION THEORY
-
8/11/2019 3-Basic Decision Analysis
3/33
Expected value criterion
Suppose you face a situation !ere you "ust c!oose#eteen alternativesA and B as follos$ AlternativeA$ %&'(''' for sure) Alternative B$ *'+ c!ance of receivin, %&-(''' and
.'+ c!ance of loosin, %/(''')
0!at is your personal c!oice1
Co"pare no Alternative B it!$ Alternative C$ *'+ c!ance of innin, %2/(3'' and
.'+ c!ance of loosin, %&4(/''
Note t!at EMV5B6 7 EMV5C6( #ut are t!ey8e9uivalent:1
Alternative C see"s to #e 8"ore ris;y: t!anAlternative B even t!ou,!t t!ey !ave t!e sa"e EMV)
Conclusion$ EMV does not take Risk into account
-
8/11/2019 3-Basic Decision Analysis
4/33
T!e ? criterion$
T!is "eans t!at you s!ould #e illin, to pay up to an in=nite
a"ount of "oney to play t!e ,a"e( #ut !y people are
unillin, to pay "ore t!an a fe dollars1
=+
+
+
=
=
=
...)8($8
1)4($
4
1)2($
2
1)2($
2
1
1k
k
k
EMV
-
8/11/2019 3-Basic Decision Analysis
5/33
T!e
-
8/11/2019 3-Basic Decision Analysis
6/33
T!e rules of actional
t!ou,!t Ho a person s!ould acts or decides rationally underuncertainty1
Anser$ #y folloin, t!e folloin, rules or axio"s$
T!e orderin, rule
T!e e9uivalence or continuity rule T!e su#stitution or independence rule
Deco"position rule
T!e c!oice rule
T!e a#ove =ve rules for" t!e axio"s for DecisionTheory
-
8/11/2019 3-Basic Decision Analysis
7/33
T!e orderin, rule
T!e decision "a;er "ust #e a#le to state !ispreference a"on, t!e prospects( outco"es( or priesof any deal
urt!er"ore( t!e transitivity property "ust #e
satis=ed$ t!at is( if !e prefers to Y( and Y to ( t!en!e "ust prefer to
>at!e"atically(
T!e orderin, rule i"plies t!at t!e decision "a;er canprovide a co"plete preference orderin, of all t!e
outco"es fro" t!e #est to t!e orst Suppose a person does not follo t!e transitivity
property$ t!e "oney pu"p ar,u"ent
-
8/11/2019 3-Basic Decision Analysis
8/33
T!e e9uivalence or
continuity rule Fiven a prospectA( B( and Csuc! t!at ( t!ent!ere existsp!ere 0 < p < 1 suc! t!at t!e decision "a;erill #e indiGerent #eteen receivin, t!e prospect Bfor sureand receivin, a deal it! a pro#a#ilitypfor prospectAand apro#a#ility of 1 p for prospect C
Fiven t!at
B$ certain equivalent of t!e uncertain deal on t!e ri,!t
p$preference probability of prospect B it! respect toprospects A and C
CBA
CBA
-
8/11/2019 3-Basic Decision Analysis
9/33
T!e su#stitution rule
0e can alays su#stitute a deal it! its certaintye9uivalent it!out aGectin, preference
or exa"ple( suppose t!e decision "a;er is indiGerent#eteen B and t!e A C deal #elo
T!en !e "ust #e indiGerent #eteen t!e to deals#elo !ere Bis su#stituted for t!eA C deal
-
8/11/2019 3-Basic Decision Analysis
10/33
T!e deco"position rule
0e can reduce co"pound deals to si"ple ones usin,t!e rules of pro#a#ilities
or exa"ple( a decision "a;er s!ould #e indiGerent#eteen t!e folloin, to deals$
-
8/11/2019 3-Basic Decision Analysis
11/33
T!e c!oice or
"onotonicity rule Suppose t!at a decision "a;er can c!oose #eteen todeals &and 2as follos$
If t!e decision "a;er prefers A to B( t!en !e "ust prefer& to 2 if and only if p& J p2) T!at is( if
In ot!er ords( t!e decision "a;er "ust prefer t!e dealt!at oGers t!e ,reater c!ance of receivin, t!e #etteroutco"e
BA
-
8/11/2019 3-Basic Decision Analysis
12/33
>axi"u" expected
utility principle et a decision "a;er faces t!e c!oice #eteen touncertain deals or lotteries & and 2 it! outco"es A&(A2( K( An as follos$
T!ere is no loss of ,enerality in assu"in, t!at L1and L2!ave t!e sa"e set of outco"esA1, A2, , An#ecause ecan alays assi,n ero pro#a#ility to t!ose outco"est!at do not exist in eit!er L1and L2)
Its not clear !et!er L1or L2is preferred
By orderin, rule( letnAAA ...21
-
8/11/2019 3-Basic Decision Analysis
13/33
>axi"u" expected
utility principle A,ain( t!ere is no loss of ,enerality as e can alaysrenu"#er t!e su#scripts accordin, to t!e preferenceorderin,
0e note t!at A& is t!e "ost preferred outco"e( !ile
An is t!e least preferred outco"e By e9uivalent rule( for eac! outco"e A i5i 7&( K( n6
t!ere is a nu"#er uisuc! t!at ' L uiL & and
Note t!at u&7 & and un7 ') 0!y1
-
8/11/2019 3-Basic Decision Analysis
14/33
>axi"u" expected
utility principle By t!e su#stitution rule( e replace eac! Ai 5i7&(K(n6in & and 2 it! t!e a#ove constructed e9uivalentlotteries
-
8/11/2019 3-Basic Decision Analysis
15/33
>axi"u" expected
utility principle By t!e deco"position rule( &and 2"ay #e reducedto e9uivalent deals it! only to outco"es 5A&and An6
eac! !avin, diGerent pro#a#ilities
inally( #y t!e c!oice rule( since ( t!e decision
"a;er s!ould prefer lottery &to lottery 2if and only if
nAA 1
==
>
n
i
ii
n
i
ii qupu11
-
8/11/2019 3-Basic Decision Analysis
16/33
Mtilities and utility
functions 0e de=ne t!e 9uantity ui5i=1,,n6 as t!e utility ofoutco"eAiand t!e function t!at returns t!e values ui
,ivenAias a utility function( i)e) u(Ai)7 ui
T!e 9uantities
are ;non as t!e expected utilities for lotteries & and
2respectively
Hence t!e decision "a;er "ust prefer t!e lottery it!a !i,!er expected utility
==
n
i
ii
n
i
ii AuqAup11
)(and)(
-
8/11/2019 3-Basic Decision Analysis
17/33
Case for "ore t!an 2alternatives
T!e previous "ay #e ,eneralied to t!e case !en adecision "a;er is faced it! "ore t!an to uncertainalternatives) He s!ould c!oose t!e one it! "axi"u"expected utility
Hence
!ere is t!e pro#a#ility for t!e outco"eAiin t!e
alternativej
==
n
ii
j
ij AupMax 1 )(argealternativbest
j
ip
-
8/11/2019 3-Basic Decision Analysis
18/33
Co"parin, expected utility criterionit! expected "onetary value criterion
T!e expected utility criterion ta;es into account #ot!return and ris; !ereas expected "onetary valuecriterion does not consider ris;
T!e alternative it! t!e "axi"u" expected utility is
t!e #est ta;in, into account t!e trade oG #eteenreturn and ris;
T!e #est preference tradeoG depends on a personsris; attitude
DiGerent types of utility function represent diGerent
attitudes and de,ree of aversion to ris; ta;in,
-
8/11/2019 3-Basic Decision Analysis
19/33
BASIC DECISION ANAYSIS
-
8/11/2019 3-Basic Decision Analysis
20/33
T!e party pro#le"
i" in,in "en,ada;anpesta ulan, ta!un) Dia"e"perti"#an,;an .lo;asi te"pat$ outdoor(indoor( teras 5porc!6
Decision
node
C!ance node
-
8/11/2019 3-Basic Decision Analysis
21/33
Nodes
Decision node$
Ber#entu; perse,i
>ela"#an,;an titi; dala" tree yan, "enyata;antiti; pen,a"#ilan ;eputusan( decision "a;er
"e"punyai ;e#e#asan penu! untu; "en,a"#il;eputusan
C!ance node$
Ber#entu; #ulat
>ela"#an,;an uncertain varia#le( decision "a;ertida; "e"punyai ;ontrol ter!adap outco"e varia#leini
-
8/11/2019 3-Basic Decision Analysis
22/33
Solvin, party pro#le"
Den,an "en,,una;an @ rules$
Orderin, rule
E9uivalence rule
Su#stitution rule
Deco"position rule
C!oice rule
-
8/11/2019 3-Basic Decision Analysis
23/33
Orderin, rule
-
8/11/2019 3-Basic Decision Analysis
24/33
-
8/11/2019 3-Basic Decision Analysis
25/33
>e"#uat decision tree
>isal;an$
-
8/11/2019 3-Basic Decision Analysis
26/33
Su#stitution rule deco"position rule
-
8/11/2019 3-Basic Decision Analysis
27/33
C!oice rule
Qadi dipili! lo;asi pesta indoor den,an pro#a#ilityuntu; "endapat;an #est outco"e ter#esar
-
8/11/2019 3-Basic Decision Analysis
28/33
Expected utility untu;setiap alternatif
-
8/11/2019 3-Basic Decision Analysis
29/33
E9uivalent >onetary orDollars ?alues
Cara lain selain"en,,una;an utilityvalue adala!"en,,una;an equivalent
mneta!y value untu;setiap outco"e)
-
8/11/2019 3-Basic Decision Analysis
30/33
Dollar value vs utility
value
Mtility functionu5x6
-
8/11/2019 3-Basic Decision Analysis
31/33
Certain e9uivalent
T!e certainty e9uivalent 5CE6 is t!e a"ount in!ic! a person is Pust indiGerent #eteenreceivin, it for sure and an uncertain or ris;yprospect t!at "i,!t eit!er pays "ore or less t!an
t!is a"ount)
T!e Certainty E9uivalent of a deal is t!e PersonalIndierent Selling Price (PISP
To =nd t!e CE of an alternative( e =rst co"puteits expected utility and t!en ta;e its inverse toconvert it #ac; into e9uivalent dollar value)
-
8/11/2019 3-Basic Decision Analysis
32/33
-
8/11/2019 3-Basic Decision Analysis
33/33
>en,una;an utility functionuntu; ;asus lain >isal;an i" "en,!adapi deal se#a,ai #eri;ut$
EM 7 '(@
top related