3. Solve the SDP problem below, assume you are maximizing. What is the optimal s

Question

3. Solve the SDP problem below, assume you are maximizing. What is the optimal strategy, and what is the optimal expected benefit given that you are in state A in t-1? It is probably easiest to mark up the pdf, or print it out, solve it, and scan it. States are "A","B","C","D". There are 3 decision stages t-1 t-2 t-3 t-4 a1,12 a1,9 a1,9 a2,1 a2,1 a2,1 a1,4 2,3 a1,4 a2,6 a2,6 5,7 5,7 C a1,5 c a1,5 5,7 a2,3 a2,3 5,7 5,7 a1,7 a1,7 a2,6 a2,6 Italic numbers after commas "" are benefits. You are maximizing the expected benefits For instance "a3,10" means you get 10$ of benefits if you choose a3. "p=5,4" means that the event outcome happens with probability 0.5, and if it happens, you get 4$ more benefit

Explanation / Answer

Let's start at t=1

Our three options are :

Hence, our first desicion at t=1 is a3

Now, at t=2

Our options at C are :

Our options at D are :

Since we are maximizing profit, we compare both values for each decision

a1 = (7.2 +7) / 2 = $7.1

a2 = (8.5 +6) / 2 = $7.25

Hence, our desicion at t=2 is a2

Now, at t=3

Our options at B are :

Our options at C are :

Our options at D are :

Since we are maximizing profit, we compare all values for each decision

a1 = (6.2 +7.2 +7) / 3 = $6.8

a2 = (10 +8.5 +6) / 3 = $8.16

Hence, our desicion at t=3 is a2

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