In this video, I’ll show how to make decisions from payoff tables using Excel or Google sheets.
The decisions will be based on these five approaches.
In the rows here we have the decision alternatives,
and, in the columns, we have the states of nature. The Maximax or Optimistic approach:
Here, I’m going to first find the maximum payoff for the first decision,
then double click the fill handle to copy it down. To easily identify the maximum of these payoffs,
I’m going to use custom formatting to highlight the cell containing it.
I’m going to use top/bottom rules, then Top 10 items.
Since I only want the maximum and not top 10, I’m going to change the input here from 10 to 1.
Then I can pick a Green Fill from the drop down here for the cell.
I’m going to centre and make them bold.
We can easily see here that the maximum payoff is 40 and it corresponds to “alternative d2”.
For the Maximin Approach, I’m going to just copy the formatting
from maximax here and paste down here. We first find the minimum for each decision
alternative and choose the maximum. So =MIN for the first alternative
Copy it down And you can see here that
the formatting is automatically applied telling us that the maximum value is -2
and it occurs for both d1 and d4. So, the conservative decision will be “d1 or d4”.
I’m again going to copy the formatting and paste for the Laplace approach.
Here we calculate the average for each decision alternatives and choose the best.
So, for the first one, =AVERAGE, select the payoffs
and copy it to the rest. The formatting is automatically applied here again
The best average payoff is 18.25 and the best decision is d5.
For the realism approach, I’m going to copy the formatting again and paste here.
We need a weighted average based on alpha being 0.3.
The weighted payoffs are calculated as alpha times the best payoff plus
1 minus alpha times the worst payoff.
So, 0.3 times the maximum
plus 1 minus 0.3, which is 0.7, times the minimum.
We see that the maximum is 9.4, corresponding to d1.
For the Minimax regret approach, we first construct a regret table
So, I’m going to copy and paste the table structure.
Since regret is the difference between the best payoff and actual payoff received,
I’m going to create a row for the best payoff for each state of nature here.
For the first regret calculation, we take the best payoff for s1
and make it an absolute cell. In this case, we want to lock
down that row 44 so I’m going to press F4 a few times till there’s only one $ sign in front of 44.
This will ensure that the max values in row 44 do not change
when we copy the formula to other cells. We now subtract the corresponding value.
ENTER. The regret is zero here
because 36 is the highest value in that column. Dragging that down computes the regrets for s1.
And dragging to the right, we have the full regret table.
Double-clicking here shows that the formula copied correctly.
Next, we find the maximum regret for each decision.
And finally, choose the minimum
of the maximum regrets which is 19 in this case.
The minimax regret decision is thus d5.
And that’s it. Thanks for watching.