Privacy policy is a must both for a web site and for an app. Go to any app or site that is similar to what you are doing, read a couple of their privacy policies and rewrite them for your own case. In many cases it will seem that you are not tracking what the user is doing or that you do not take any personal data from the user so, why bother with a privacy policy at all? It turns out that nowadays people know that they are being spied upon and expect to be tracked across the web and the apps. They are aware of the negative possibilities and want to know what are you doing with the data they produce using an app.
If in a game you are tracking what the users do “in order to improve game experience”, tell them what will you do with such data and tell them also whether you will be selling those data to third parties or not. If you are showing third party ads say from AdMob, be sure to incorporate a notice about that in your privacy policy. Ads agencies will usually provide you a paragraph or two that you should put into your privacy policy so it is not so difficult to create.
Most users will never read any of the “policy” documents that you should have in the app but you should nevertheless have them. In my apps, I have Privacy Policy, Copyright Policy, Terms of Service, Anti Spam, and Disclaimer Policy documents. Some are very long, some are one or two paragraphs long but important nonetheless. The good news is that once you create them for one app, you can transfer them almost unchanged to all other apps of yours so it is not such a great problem in the long run.
And of course, you may want to search for the privacy policy creating sites that will do it for free. For best effect, you may want to combine your original draft with the content that these sites give you.
Policy documents should protect both you and your customers / users. In the excitement of going to be published creating them looks like a trivial and unneeded chore to do, and yet if you are in this as a business, but they must be there.