Question

Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below. Answer questions a, b, and c. 1/3 1/3 Payoff 1 Payoff 2 PayOff 3 1/3 4 0.30 Payoff 4 0.50 Payoffs Altem ative A 0.20 PayOff 6 9 1/3 1/3 1/3 PayOff 7 PayOff 8 PayOff 9 Alternative B 0.30 Payoff 10 0.50 8 Payoff 11 0.20 Payoff 12 1/2 6 Payoff 13 1/2 Payoff 14

Answer 1

(i) value of node 1 = 1/3* ( sum of payoff 1, 2 and 3) =10/3

Value at node 4 = max [ payoff 4, value of node 1] = [2,10/3] =10/3

(ii) Value of node 2 = 1/3 *[ sum of payoffs of 7,8,9] = 1/3 [ -3-4+7]=0

Value of payoff 10=6

Value of node 5 = Max [ value of node 2, value of payoff 10]=6

Value of payoff 3 = 1/2 * ( value of 13 + vaue of 14] = 0.5 *(7+3) =5

Value of payoff 12=-3

Value of node 6 = max [ Value of payoff 12, Value of payoff 3] = Max [ 5,-3]=5

Valur of node 8 = 0.3*value of payoff at node 5 + 0.5* payoff 11+0.2*Value of node 6

=0.3*6+0.5*5+0.2*5 = 5.3

Value of node 7 = 0.3*value at node  4 + 0.5*payoff 5+0.2*payoff 6

= 0.3*10/3 + 0.5*8+0.2*4 = 5.8

Best course of action is alternative A as it has highest payoff