I guess I don’t see what’s so wrong with “you can’t do all the actions in your action space,” which just seems like another way of saying “this action space isn’t the right formalization of the problem.”
I disagree. Sometimes your entire payoffs also change when you change your action space (in the informal description of the problem). That is the point of the last example, where precommitment changes the possible payoffs, not only restricts the action space.
I guess I don’t see what’s so wrong with “you can’t do all the actions in your action space,” which just seems like another way of saying “this action space isn’t the right formalization of the problem.”
I disagree. Sometimes your entire payoffs also change when you change your action space (in the informal description of the problem). That is the point of the last example, where precommitment changes the possible payoffs, not only restricts the action space.