Question

1/3 1/3 1/3 Payoff 1 PayOff 2 Payo ff 3 0.3 PayOff 4 0.50 Payo ff 5 Alternative A 0.20 Payo ff 6 9 1/3 1/3 1/3 PayOff 7 PayO ff 8 Payoff 9 Alternative B 0.30 PayOff 10 0.50 8 Payoff 11 0.20 PayOff 12 1/2 PayOff 13 3 1/2 PayOff 14

Answer 1

a) Value at Node 1 = 1/3* payoff 1+ 1/3*payoff2 + 1/3*payoff3 = 6/3+8/3 +8/3 = 22/3 = 7.33

Value at Node 4 = payoff4+Node 1 Value = -6+7.33 = 1.33 = 4/3

b) Node 2 = payoff7/3 + payoff8/3 + payoff9/3 =(-4+4+1)/3 = 1/3

Value at 5 = Node 2 value + payoff10 = 1/3+ 6 = 19/3

Node 3 = 1/2 * payoff13 + 1/2 * payoff14 = 7/2 + 1 = 9/2

Node 6 = Node3 value + Payoff12 = 9/2 -3 = 3/2

Node 8 value = 0.3*node 5 + 0.5*payoff11 + 0.2 * Node 6 = 0.3*19/3 + 0.5*2 + 0.2*3/2 = 1.9+1 +0.3 = 3.2

c)

Alternative A = node value at 7 = 0.3* node 4 + 0.5 * payoff5 + 0.2*payoff6 =0.3*4/3 + 0.5 * 5 + 0.2 * 4 =0.4+2.5+0.8 = 3.7

Alternative B = node 8 value = 3.2

As Value for Alternative A > value of alternative B

So best course of action or decision is to select alternative A