Minimax
Pick the strategy that holds the other side's best achievable payoff as low as possible, which in a two-player zero-sum game yields the same number and the same play as maximin.
Often misread asTreating maximin and minimax as the same thing because they coincide in zero sum games, then carrying that over to games that are not zero sum, where they come apart.
How to see it
Holding them to a ceiling rather than yourself to a floor
The mirror image of guaranteeing yourself a floor is holding the other side to a ceiling: choose so as to make the best they can manage as small as possible. In a two person game where your gain is exactly their loss, the floor you can guarantee and the ceiling you can impose turn out to be the same number.
The checkOne is about your own worst case, the other about limiting theirs. They agree only when one player's gain is exactly the other's loss.
Try itIn matching pennies, work out the most you can guarantee yourself and the least you can hold your opponent to. Once mixing is allowed both come to zero. Now try the same in the stag hunt and watch the two numbers separate.
Games that show it
Know these first
Easily confused with
Sources
- von Neumann, J. (1928). Mathematische Annalen 100(1), 295-320.
- von Neumann, J. & Morgenstern, O. (1944). Princeton UP.
- Luce, R. D. & Raiffa, H. (1957). Wiley. Covers duels and timing games.