Welcome! In this brief video, we will be discussing decision making without
probabilities.
In this first part, we will consider Maximax
or the optimistic approach, the maximin
also known as conservative or pessimistic approach, and
the minimax regret approach to decision-making.
The table seen here
is referred to as a payoff table or decision table.
the alternate is on the left here
in the rows are referred to as
Decision Alternatives. They are the options available for the
decision maker to choose from
We will assume that the decision maker can
only choose one of these alternatives - invest in bonds
stocks, or mutual funds.
In the columns we have the economic conditions.
Since the decision maker does not have control over these,
we refer to them as states of nature
or outcomes. The values in the table
are called payoffs. They could be profit,
cost, distance, time, and so on.
In this example we treat them as profits.
The Maximax or Optimistic approach
Using this optimistic approach, we choose the alternative
with the best possible payoff. Looking at Bonds
the best payoff is 45. The best is 70 for stocks,
and the best is 53 for mutual funds.
The overall best is 70. Therefore the decision is to invest in stocks.
The maximin or conservative approach. Using this pessimistic approach
we choose the alternative with the best of the worst
payoffs. We first choose the the worst payoff
in each alternative and then choose the best of the worst.
Looking at Bonds, the worst payoff is 5,
the worst is -13 for stocks
and the worst is -5 for mutual funds.
The best of these is 5.
Therefore the pessimistic or conservative approach
is to invest in bonds. The minimax regret approach.
Using this approach which choose the alternative
with the minimum of all maximum regrets
across all alternatives. Regret,
also known as opportunity loss is the difference between the best payoff
in a particular state of nature and the actual
payoff received. For example, if the economy is growing,
the best payoff is 70. If we happened to have invested in bonds,
then the regret will be 70 - 40
which is 30. If we invested in stocks
then there is no regret. If we invested in mutual funds,
then the regrets is 70 minus 53 which is 17.
Again, if the economy stable, the best payoff is 45,
so if we invested in bonds, there is no regret, the regret
is 45 - 30 if we invested
in stocks, if we invested in mutual funds
there is also no regret. For declining economy
the best payoff is 5. If we invested in bonds,
there is no regret; if we invested
in stocks the regret is five minus -13 which is
18; if we invested in mutual funds, the regret is 5 minus -5
which is 10.
Here is the regret table.
Since the decision is to be made
based on minimax regret, we first determine
the maximum regret for each alternative and then choose the minimum.
For bonds, the maximum
regret is 30. For stocks
it is 18, and for mutual funds,
it is 17. The minimum of these maximum regrets is 17.
The decision is to invest in mutual funds.
See you in part 2.
Thanks for watching!