Given the payoff table listed below, please answer: #1 #2 #3 #4 A 1 0 1 6 B 1 5
ID: 418629 • Letter: G
Question
Given the payoff table listed below, please answer:
#1 #2 #3 #4
A 1 0 1 6
B 1 5 4 2
C 3 2 2 3
State of Nature
Alternative
(a).If somehow you find out for certain that state of nature #4 is going to occur, which
alternative will you select?
(b). If you are uncertain which state of nature will occur, and use the maximin criterion, which
alternative will you select?
(c). If you are uncertain which state of nature will occur, and use the maximax criterion, which
alternative will you select?
(d). If you are uncertain which state of nature will occur, and use the Laplace criterion, which
alternative will you select?
(e). If you feel that P(#1)=0.4, P(#2)=0.3, P(#3)=0.2, and P(#4) =0.1, which alternative will you
select? What is your expected payoff under certainty? What is your expected value of perfect
information?
Explanation / Answer
(a) A will be selected, the payoff being the highest.(6)
(b) Under maximin criteria, the alternative is the best among the worst, i.e. highest of 0,1 and 2, ie. 2, which corresponds to C
(c) Under maximax criteria, the choice will be maximum of maximum value which is highest of 6,5 and 3 which is 6, and corresponds to A.
(d) Under Laplace criterion, equal probability will be assigned to each event i.e. 0.25 to each
Payoff for A = 0.25+0+0.25+6x0.25 = 2
Payoff for B = 0.25 ( 1+5+4+2) = 3
Payoff for C = 0.25 (3+2+2+3) =2.5
Choice is B as the payoff is highest ( 3)
(e) Under new condition
Payoff for A = 0.4x1+0x0.3+0.2x1 + 0.1x6 = 1.2
Payoff for B = 0.4x1 +0.3x5+0.2x4 + 0.1x2 = 2.9
Payoff for C =0.4x3 + 0.3x2+0.2x2 +0.1x3 =2.5
Payoff for B is highest, therefore B is the choice.
Payoff under certainty = 0.4x3+0.3x5+0.2x4+0.1x6 =4.1
Expected value of perfect info. = Payoff under certainty - max. payoff under uncertainty
= 4.1-2.9 =1.2
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