Unfriendly competition which may involve the setting up of more magazines (4,4)
I believe the answer is:
arms race
'unfriendly competition' is the definition.
'arms race' can be an answer for 'competition' (arms race is a kind of competition). I'm unsure of the 'unfriendly' bit.
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for arms race that I've seen before include "Weaponry competition" , "Potentially dangerous competition" , "rush to war" , "dangerous situation escalating" , "Weapon competition" .)