My name is Erik and I'm a Senior Analyst-Programmer with more than 15 years of experience combined with 6 years of being a Sales Call Center expert.
It does depends on specific factors. Some of them are: Cost of application, quality of the game, is it a unique game, is there geographical limitations, how agressive is your ads campaigns, etc. The average cost to users acquisition is variable depending on the product sold. Some applications/games cost almost nothing to market (like Pokemon Go!) and others that has more challenges.
If you want to discuss on a call about ways increasing your users (and revenues if it applies) and how to do efficient marketing for your game, don't hesitate to schedule a call with me.
Cost per user acquisition of iPhone game apps really depends on the game and the subject matter of the game.
Here's some general data on the topic of cost per installs:
iOS app CPI Globally – $1.24
iOS app CPI in US – $1.64
iOS app Cost Per Loyal User in US – $2.78
iOS app CPI in Europe – $1.4
iOS app CPI in Asia – $0.90
Getting a user to install the app is one step. Getting them to register is the next step.
I will need to know more about the game to speak more deeply to the details, but if it's a general game that's fun to use, and looks appealing, my hunch is you should be able to hit to these CPI numbers.
How to acquire the users is the next strategic question.