Not understanding the concept of payoff tables. Need help with the following: Pr
ID: 403487 • Letter: N
Question
Not understanding the concept of payoff tables. Need help with the following:
Problem 1 -
Use the following Payoff Table:
State of Nature ----------Yes No
Small $10* 30
Medium 20 40
Med.-Large 30 45
Large 40 35
Ex-Large 60 20
*PV for profits ($000)
What is the Maximin strateygy: Small, Medium, Med-Large, Large, or Ex-Large?
Problem 2 -
Use the following Payoff Table:
State of Nature ----------Yes No
Small $10* 30
Medium 20 40
Med.-Large 30 45
Large 40 35
Ex-Large 60 20
*PV for profits ($000):
The minimax regret strategy would be:
Explanation / Answer
Maximin is the maximum of the minimum payoffs
so we should choose large as it has the maximum of every sections minimum value
small is min( 10, 30 ) = 10
medium = 20
med-large = 30
large = 35
ex-large = 20
as the max of all the above entries is 35 large, large is the Maximin strategy.
Problem 2 )
We have to choose an option where regret will be the least with respect to other options.
for scenario yes.
small regre it 60 - 10 = 50
med regret = 60 - 20 = 40
med -large = 30
large = 20
ex large = 0
for scenario no
small regret is 45 - 30 = 15
medium = 45 - 40 = 5
med - large = 45-45 = 0
large = 10
ex-large = 25
now the max regrets in each case depending
small is max( 50, 15 ) = 50
med is max( 40, 5 ) = 40
med-large is ( 30,0 ) = 30
large is ( 20,10 ) = 20
exlarge is ( 0, 25 ) = 25
The minimum of above is for large = 20
Hence large has to be chosen here too
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