No but it's not because competition isn't allowed, but because users are no more likely to manually switch browsers on their phones than they are on the desktop. Google's emphasis on Chrome in recent versions of Android is certainly a step in the right direction here but it will likely be another two years before the majority of Android users are running a really first-class browser thanks to the slow uptake of Android updates.

But I really think the discoverability advantages people cite for the app stores is highly overrated. If you can squeeze your way into the top twenty then maybe there's some real benefit but for most apps the app store is just an opaque box with primitive SEO and analytics.