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#GameTheory question for everyone...
Is there a name for when an optimal strategy is avoided because the optimal strategy is easily defended against when you know the person is using it in the first place?
Or the reverse, where someone might intentionally use a very poor strategy specifically because the user would never expect a user to pick a poor strategy and thus, at least when assumed it wont be used, becomes a strong strategy?
That would mean that it's not an optimal strategy, no?
This reasoning makes me think of probabilistic strategies: for some classes of games there is no best deterministic strategy, but there _is_ a best probabilistic one. See https://en.wikipedia.org/wiki/Strategy_(game_theory)#Mixed_strategy for something related.
@robryk Depends.
Might work better as an example.
Imagine a game of battleship but where one player is firing the other controls the ships. So we are trying to find an optimal firing pattern vs optimal ship placement.
By default there is no strategy for ship placement I can think of other than to make sure ships arent adjacent. So you have a more or less random placement.
But if ship placement is random then since there are more ship layouts that overlap closer tot he center of the board as opposed to near the edges, then the optimal firing strategy would be to avoid the edges, with the 4 corner spaces being the least favorable target to hit. So the optimal stregy here is to more or less focus away from the walls.
it should also be noted that while random placement does tend to cover squares near the center more often, there is a strategic reason to not prefer walls and intentionally place ships near the center too. That is, once a strike on a ship is made it is easier to guess the orientation of the ship and destroy it for ships next to walls than it is for ships away from walls. So for this reason as well it is generally optimal to place ships asway from walls.
Anyway as you can see this chain of logic can go on as per the premise.
@freemo @robryk Ok, not adjacent.
This is exactly the kind of game Dr. John Nash was describing. His Nobel Prize winning paper on the subject is here: https://www.cs.upc.edu/~ia/nash51.pdf
