PLEASE ANSWER ALL THE PARTS STEP BY STEP #3. Consider the following payoff table
ID: 3124149 • Letter: P
Question
PLEASE ANSWER ALL THE PARTS STEP BY STEP
#3. Consider the following payoff table (where the payoffs are measured in $).
Value
State 1
State 2
State 3
Act 1
10
5
0
Act 2
0
20
0
Act 3
5
10
20
Probabilities
.3
.4
.3
#3a. The simple pessimist uses the maximin value decision rule. Which act would the simple pessimist choose? (Show your work.)
#3b. The sophisticated pessimist uses the minimax regret decision rule. Which act would the sophisticated pessimist choose? (Show your work.)
#3c. The risk neutral decision maker uses the maximum expected value decision rule. Which act would the risk neutral decision maker choose? (Show your work.)
Value
State 1
State 2
State 3
Act 1
10
5
0
Act 2
0
20
0
Act 3
5
10
20
Probabilities
.3
.4
.3
Explanation / Answer
3A. Under Maximin criteria, the minimum payoff under each alternative is identified. Then, the alternative with maximum of all minimum payoff is identified as a decision criteria.
Minimum payoff with act 1 = 0
Minimum payoff with act 2 = 0
Minimum payoff with act 3 = 5
Since maximum payoff is 5 with act 3. So, act 3 will be selected as the best act.
3B. In this criteria, maximum regret with each alternative is calculated. Then, alternative with minimum of the maximum regret is calculated as the best alternative.
In the given table, values are calculated using the maximum payoff in each scenario and subtracting the all payoff from maximum payoff in that scenario. For example, 10 is best payoff in state1. So, values 10, 0 and 5 are subtracted from 10 and give values of 0, 10 and 5 respectively. Similarly, it will be done with other scenarios.
Since the minimum of maximum regret is 10. So, Act 3 will be selected.
3C. Expected payoff value of act 1 = .3*10+.4*5+.3*0 = 5
Expected payoff value of act 2 = .3*0+.4*20+.3*0 = 8
Expected payoff value of act 3 = .3*5+.4*10+.3*20 = 11.5
Since the expected value is 11.5, with act 3. So, act 3 will be selected under this criteria.
Value State 1 State 2 State 3 Maximum Regret Act 1 0 15 20 20 Act 2 10 0 20 20 Act 3 5 10 0 10Related Questions
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