Convert “$x” into “something Alice wants”. Alice doesn’t really want $x, she wants a new car, a house, a vacation, a new machine for her factory.
Now “They want to (add, prevent from decay) as many edges as possible” becomes “They want to encourage different parties to lend each other things they want”.
Now “They want to (add, prevent from decay) as many edges as possible” becomes “They want to encourage different parties to lend each other things they want”.