Question

Consider the following diagram. What action is the CEO taking? Good outcome 50% (950,105) Risky choice 50% (-10,45) Bad outcome Setup hierarchy Safe choice (350,65) CEO Good outcome 50% (1000,115) Delegate Risky choice 50% (40,55) Bad outcome Manager Safe choice (400,90) Setup Hierarchy Delegate

Answer 1

Decision Tree

Excel Formulation:

A B C D E F G H K 1 2 Outcome 1 Outcome 2 Outcome 1 Outcome 2 3 4 Good Outcome 950 105 115 Risky 0.5 Choice 0.5 0.5 Good Outcome 1000 Risky Choice 0.5 Bad Outcome 40 5 Bad Outcome -10 45 55 6 7 Risky Choice =SUMPRODUCT($B$4:$B$5,04:05) =SUMPRODUCT($B$4:$B$5,E4:E5) Risky Choice =SUMPRODUCT($B$4:$B$5,14:15) =SUMPRODUCT($B$4:$B$5,K4:K5) 8 9 =D7 0.5 =J7 =K7 Risky Choice Safe Choice =E7 65 Manager Risky Choice Safe Choice 350 0.5 400 90 Set Up Hierarchy =SUMPRODUCT($B$10:$B$11,D10:011) -SUMPRODUCT($B$10:$B$11,E10:E11) Manager =SUMPRODUCT($B$10:$B$11,J10:J11) =SUMPRODUCT($B$10:$B$11,K10:K11) 10 Set Up 0.5 11 Hierarchy 0.5 12 13 14 15 16 17 CEO 18 19 =C13 =D13 =E13 =K13 =113 =J13

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Solution:

A B D E F G H K L 1 Outcome 1 Outcome 2 Outcome 1 Outcome 2 950 115 2 3 4 5 6 7 Risky Choice 50% Good Outcome 50% Bad Outcome 105 45 50% Good Outcome Risky Choice 50% Bad Outcome 1000 40 -10 55 Risky Choice 470 75 Risky Choice 520 85 8 9 10 470 75 520 85 50% Set Up Hierarchy 50% Risky Choice Safe Choice Manager 50% 50% Risky Choice Safe Choice 350 65 400 90 Set Up Hierarchy 410 70 Manager 460 87.5 11 12 13 14 15 16 17 18 410 70 CEO Set Up Hierarchy Manager 460 87.5 19

From the above analysis, it can be inferred that going for a ‘delegate’ option has a higher utility/ expected return. So, the CEO should select the ‘Delegate’ option.

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