So, why didn't Arsenal buy a player on deadline day?
For one, it's harder than you think to sign players. Convincing them takes a lot and Arsenal have nothing to show in the last six years to attract players.
And to still be able to sign their targets is a huge achievement for Wenger.
Secondly, Wenger will sign players only if he is sure of them. He won't splash the cash needlessly. The player he wanted may not be available at all... or the club may have priced him out. Take for example the 25 million pound signing of David Luiz. How did that work out? Defenders are absolutely mint in Europe and Arsenal don't have that spending policy. Actually, they never have.
Arsenal will not be successful by just buying a very expensive player, and Wenger knows that, and that's why he didn't sign anyone.