Wolfkrone Monument: "While this card is ready in your staging area, after a player plays an attack, that attack gets -1 damage or -1 speed (your choice)

Arrogant and Insolent: "R Commit, discard 1 card: After you reduce the damage of an attack, ready your character"

So the question is, can I respond with A&I to Wolfkrone's static ability?

Or at least could I respond with it after I play an attack and choose to reduce it's damage?

Also another question off the topic, can the ability on Cage arena be played by both players on the same attack ie. Im playing hilde, I use it to reduce the damage of my attack, after I use her ability my opponent uses Cage to reduce my attack to 1?
I wasnt sure if the each E of a card my only be played once per enhance step applies or not since stuff in the past has said "Each player my only play this ability once per Enhance step" like on Whereabouts Unknown.

@Cage Arena: The ability may be played exactly once per Enhance Step, regardless of which player plays it.

Dunno about the other Q

Arrogant and Insolent responds to the damage of a attack being reduced not the effect that does the reduction so you can.

The important distinction with A&I is that it's responding to an actual damage reduction occurring. You're thinking of abilities that respond to an ability being played, which continuous abilities never are, but A&I has nothing to do with an ability being played, it's just looking for a particular type of effect.

Cool, thats basically what I figured but a local scout had said different so I figured its always better to check if in dought. Thanks for the help guys.