(Well, sort of. The minimax and maximax principles require only that we measure value on an ordinal scale, whereas the optimism-pessimism rule requires that we measure value on an interval scale.)
I’m using this as an introduction to decision theory so I might be wrong, and I’ve read that ‘maximin’ and ‘minimax’ do have different meanings in game theory, but you exclusively use the term ‘maximin’ up to a certain point and then mention a ‘minimax principle’ once, so I can only imagine that you meant to write ‘maximin principle.’ It confused me. It’s probably best to stick with one or the other.
Also, thanks for the introduction.
ETA: I found a typo.
Usually, it is argued that each of the axioms are pragmatically justified because an agent which violates the axioms can face situations in which they are guaranteed end up worse off (from their own perspective).
should be:
Usually, it is argued that each of the axioms are pragmatically justified because an agent which violates the axioms can face situations in which they are guaranteed to end up worse off (from their own perspective).
Minimax is equivalent to maximin in a zero sum game because every resource I win you lose out on. However, in non-zero games which encourage cooperation this is no longer case. Take for example a scenario in which we share some land. Let’s assume I have one third and you have two. If I water your crops as well as my own every other day you have agreed to water mine on the other alternate days when I must look after my kids. If I don’t water your crops you won’t water mine back but you don’t have any kids so you’d actually be able to water every day without me although you’d rather hang out with your friends at the pool if you could. If I want to minimise the maximum (minimax) utility you get I wouldn’t water your crops at all and force you to water every day. Of course you’d resent me for this and wouldn’t water my crops so I’d end up with no crop. If I want to maximise the minimum (maximin) crop yield for myself, I’ll have to water your crops too even though you have twice as many crops as me and you’ll get to hang out with your friends as well!
I’m using this as an introduction to decision theory so I might be wrong, and I’ve read that ‘maximin’ and ‘minimax’ do have different meanings in game theory, but you exclusively use the term ‘maximin’ up to a certain point and then mention a ‘minimax principle’ once, so I can only imagine that you meant to write ‘maximin principle.’ It confused me. It’s probably best to stick with one or the other.
Also, thanks for the introduction.
ETA: I found a typo.
should be:
Minimax is equivalent to maximin in a zero sum game because every resource I win you lose out on. However, in non-zero games which encourage cooperation this is no longer case. Take for example a scenario in which we share some land. Let’s assume I have one third and you have two. If I water your crops as well as my own every other day you have agreed to water mine on the other alternate days when I must look after my kids. If I don’t water your crops you won’t water mine back but you don’t have any kids so you’d actually be able to water every day without me although you’d rather hang out with your friends at the pool if you could. If I want to minimise the maximum (minimax) utility you get I wouldn’t water your crops at all and force you to water every day. Of course you’d resent me for this and wouldn’t water my crops so I’d end up with no crop. If I want to maximise the minimum (maximin) crop yield for myself, I’ll have to water your crops too even though you have twice as many crops as me and you’ll get to hang out with your friends as well!