Currently AAM - attempts to set a 3rd party cookie for mobile devices. Most mobile devices including all iOS reject 3rd party cookies.
Adobe offer the current work arounds to this issues :-
1) Client can set their own ID for those using mobile devices (requires authentication). For many websites including publishers this solution does not scale.
2) Work with a thrid party e.g Tapad or Drawbridge to establish links from your AAM desktop traffic to mobile devices mapped in their data set and target them via their services.
For publishers neither solution works well. Publishers have up to 50%+ of their web traffic on mobile devices and they need to be able to identify those users across multiple domains and target those users within that session on their 1st party media. I believe this is only possible if Adobe deploy their own finger printing solution to achieve this. Currently Adobe are behind compared to other DMP's and mobile detection and targeting in this area.