Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I try to understand the way to finding the minimax solution to zero-sum game.

The following example is takes from Wikipedia. Minimax

enter image description here

Wikipedia: The following example of a zero-sum game, where A and B make simultaneous moves, illustrates minimax solutions.Suppose each player has three choices and consider the payoff matrix for A displayed at right. Assume the payoff matrix for B is the same matrix with the signs reversed (i.e. if the choices are A1 and B1 then B pays 3 to A). Then, the minimax choice for A is A2 since the worst possible result is then having to pay 1, while the simple minimax choice for B is B2 since the worst possible result is then no payment.

Question: Why the minimax choice for A is actually A2, the worst possible result is actually A3 (-4), and the worst possible result for B is B3 (+4). In addition the wording "simple minimax choice for B" is very confusing, is it different from the standard minimax choice?

share|improve this question

2 Answers 2

up vote 2 down vote accepted

The worst A takes when taking (across the rows):

  • A1: -2
  • A2: -1
  • A3: -4

The minimum loss is A2.

The worst B takes when taking (along the columns):

  • B1: -3
  • B2: 0
  • B3: -4

It is best for B to pick B2.

Does that help? :)

share|improve this answer

It is A2 because the following. A asks oneself "What is the worst thing that can happen to me if I play A1?" The answer to that is -2. "What is the worst thing that can happen to me if I play A2$" The answer to that is -1. And finally "What is the worst thing that can happen to me if I play A3" The answer to that is -4. Hence, I'm better off in a minimax sense if I play A2. The other thinks the same, her payoffs tho are just the negatives of those above (since one pays them the other receives)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.