Notes on Minimax, Maximin and Maximax

Notes on Maximin, Maximax and Minimax (Regret criterion)

• Used when probabilities of events are unknown
• Based on the attitude of the investor

Maximin

• Investors aim to maximise minimum return, hence the name Maximin.

• Under this method the decision maker assumes the worst possible outcome and hopes to maximise that outcome, thus chooses the largest pay-out under the “worst” circumstances
• It is a pessimistic approach

Maximax

• It is a more optimistic approach
• Investors seek to maximise the maximum return hence the name Maximax.
• Under this method decision maker will assume the best outcome and seek to maximise it

Minimax or Regret Criterion

• This is a more neutral approach
• Under this approach the decision maker simply aims to minimise maximum regret hence the name minimax.
• This regret could be defined as the financial gain between different outcomes, and can be identified using opportunity costing

Example

Peter is a budding entrepreneur who is interested in starting a one of a kind digital technology business, he is torn between two high end machines that he could possibly use. however due to a lack of such firms in the market, the uncertainties that would affect the demand of the service is difficult to predict. The following are the possible outcomes

Recommend a decision based on the use of the Maximin, Maximax and regret criteria approaches.

 Income generated by the use of machines under different events

Under Maximin, the decision maker here Peter will assume the worst outcome will occur and try to maximise the return of such a situation, thus under low demand

Assuming low demand, he sees that

Machine A shall provide a turnover of $70,000 and Machine B a turnover of $10,000

Peter shall choose to use Machine A

Under Maximax, the decision maker here Peter will assume the best outcome will occur and try to maximise the return of such a situation, thus under high demand

Assuming high demand, he sees that

Machine A shall provide a turnover of $100,000 and Machine B a turnover of $250,000

Peter shall choose to use Machine B

Under Minimax, the decision maker here Peter will try to minimise maximum regret.

To do this we must make a regret table by looking at the initial schedule

Under this Peter would want to minimise his maximum regret so he would choose to go with Machine B as the maximum regret is lower than the regret of choosing Machine A.

...