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Decision Analysis 1: Maximax, Maximin, Minimax Regret - YouTube
Channel: Joshua Emmanuel
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Welcome!
In this brief video, we will be discussing decision making without
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probabilities.
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In this first part, we will consider Maximax
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or the optimistic approach, the maximin
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also known as conservative or pessimistic
approach, and
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the minimax regret approach to
decision-making.
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The table seen here
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is referred to as a payoff table or
decision table.
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the alternate is on the left here
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in the rows are referred to as
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Decision Alternatives. They are the
options available for the
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decision maker to choose from
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We will assume that the decision maker
can
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only choose one of these alternatives -
invest in bonds
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stocks, or mutual funds.
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In the columns we have the economic
conditions.
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Since the decision maker does not have
control over these,
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we refer to them as states of nature
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or outcomes. The values in the table
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are called payoffs. They could be profit,
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cost, distance, time, and so on.
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In this example we treat them as profits.
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The Maximax or Optimistic approach
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Using this optimistic approach, we choose the alternative
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with the best possible payoff. Looking at
Bonds
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the best payoff is 45. The best is 70 for stocks,
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and the best is 53 for mutual funds.
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The overall best is 70. Therefore
the decision is to invest in stocks.
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The maximin or conservative approach.
Using this pessimistic approach
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we choose the alternative with the best
of the worst
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payoffs. We first choose the the worst payoff
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in each alternative and then choose the
best of the worst.
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Looking at Bonds, the worst payoff is 5,
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the worst is -13 for stocks
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and the worst is -5 for mutual funds.
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The best of these is 5.
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Therefore the pessimistic or
conservative approach
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is to invest in bonds. The minimax regret approach.
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Using this approach which choose the alternative
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with the minimum of all maximum regrets
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across all alternatives. Regret,
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also known as opportunity loss is the
difference between the best payoff
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in a particular state of nature and
the actual
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payoff received. For example, if the
economy is growing,
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the best payoff is 70. If we happened to
have invested in bonds,
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then the regret will be 70 - 40
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which is 30. If we invested in stocks
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then there is no regret. If we invested
in mutual funds,
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then the regrets is 70 minus 53 which
is 17.
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Again, if the economy stable, the best payoff is 45,
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so if we invested in bonds, there is no
regret, the regret
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is 45 - 30 if we invested
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in stocks, if we invested in mutual funds
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there is also no regret. For declining
economy
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the best payoff is 5. If we invested in
bonds,
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there is no regret; if we invested
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in stocks the regret is five minus -13
which is
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18; if we invested in mutual funds, the
regret is 5 minus -5
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which is 10.
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Here is the regret table.
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Since the decision is to be made
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based on minimax regret, we first
determine
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the maximum regret for each alternative and
then choose the minimum.
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For bonds, the maximum
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regret is 30. For stocks
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it is 18, and for mutual funds,
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it is 17. The minimum of these maximum
regrets is 17.
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The decision is to invest in mutual funds.
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See you in part 2.
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Thanks for watching!
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