Maximax, Maximin, Minimax Regret, Expected Value

오늘 이야기할 키워드는 Maximax, Maximin, Minimax Regret, Expected Value이다. 오늘 포스팅을 통해 무슨 의미를 담고 있는지 알아보자.

 

 

 

 

There are 4 key decision rules with different approaches

• Maximin
• Maximax
• Minimax regret
• Expected value

 

Payoff Table

	Probability	Option
Demand		A	(R)	B	(R)	C	(R)
High	0.2	9	0	8.7	0.3	8.6	0.4
Medium	0.7	7	0.2	7.2	0	6.2	1
Low	0.1	-5	9.3	4.3	0	-5.3	9.6

 

Regret Table

	A	B	C
High	0	0.3	0.4
Medium	0.2	0	1
Low	9.3	0	9.6

 

 

 

1. Maximin (Risk averse)

• Maximize the minimum payoff (Best of Worst)
• Optimistic
• Option B

 

2. Maximax (Risk seeker)

• Maximize the maximum payoff (Best of Best)
• Conservative or Pessimistic
• Option A

 

3. Minimax Regret

• Minimizes the maximum regret 
• Regret = opportunity loss (best payoff - payoff received)
• Option B

 

4. Expected Value (Risk neutral)

• Select the highest expected value
• Consider the probability of outcomes
• Option B

Expected Value
A: (0.2 * 9) + (0.7 * 7) + (0.1 * -5) = 6.2
B: (0.2 * 8.7) + (0.7 * 7.2) + (0.1 * 4.3) = 7.21
C: (0.2 *  8.6) + (0.7 * 6.2) + (0.1 * -5.3) = 5.53