If the agent doesn’t know in advance what trades they will be offered or is incapable of backward induction, then their pursuit of a dominated strategy need not indicate any defect in their preferences. Their pursuit of a dominated strategy can instead be blamed on their lack of knowledge and/or reasoning ability.
But then wouldn’t your proposed policy be dominated by choosing to be indifferent between options with gap, because it works better without knowing trades in advance, and doesn’t work worse otherwise?
Nice point. But making your preferences complete won’t protect you from pursuing dominated strategies if you don’t know what’s coming.
For example, suppose at node 1 you face a choice between taking A and proceeding to node 2. You think that at node 2 you’ll face a choice between A- and A+. So, you proceed to node 2, with the intention of taking A+. But you were mistaken. At node 2, you face a choice between A- and A--. You take A-.
In that case, you’ve pursued a dominated strategy: you’ve ended up with A- when you could have had A. But your preferences are not to blame. Instead, it was your mistaken beliefs about what options you would have.
My intuition was something like “you would get better satisfaction of preference in expectation even if you are uncertain about the future”, but I guess it doesn’t exactly work without first defining utility function. But what about first choosing between A- and B-, and then between A or B- in A- branch, and B or A- in B- branch—this way you get (A|B-|B|A-) with gaps vs. (A|B) in indifference case—wouldn’t the mixture with worse variants intuitively be worse than one with only good ones even if we can’t strictly say that incomplete preferences are contradicted?
But then wouldn’t your proposed policy be dominated by choosing to be indifferent between options with gap, because it works better without knowing trades in advance, and doesn’t work worse otherwise?
Nice point. But making your preferences complete won’t protect you from pursuing dominated strategies if you don’t know what’s coming.
For example, suppose at node 1 you face a choice between taking A and proceeding to node 2. You think that at node 2 you’ll face a choice between A- and A+. So, you proceed to node 2, with the intention of taking A+. But you were mistaken. At node 2, you face a choice between A- and A--. You take A-.
In that case, you’ve pursued a dominated strategy: you’ve ended up with A- when you could have had A. But your preferences are not to blame. Instead, it was your mistaken beliefs about what options you would have.
My intuition was something like “you would get better satisfaction of preference in expectation even if you are uncertain about the future”, but I guess it doesn’t exactly work without first defining utility function. But what about first choosing between A- and B-, and then between A or B- in A- branch, and B or A- in B- branch—this way you get (A|B-|B|A-) with gaps vs. (A|B) in indifference case—wouldn’t the mixture with worse variants intuitively be worse than one with only good ones even if we can’t strictly say that incomplete preferences are contradicted?