Did you purposefully misunderstand that sentence or was it simply not clear? To complete the sentence in an unambiguous way 'alternative os for apple mobile hardware'.

Right, but so what? If there's alternative hardware, then there's an alternative OS; nobody is forced to use Apple mobile hardware, nobody is forced to use iOS. The fact that you can't use arbitrary operating systems on arbitrary hardware doesn't mean that Apple has a monopoly.

I begin to question whether you understand what "alternative" means in the context of the interaction between hardware and software. It's a somewhat gray area, sure, but it's not that gray. There are many, many, many different mobile devices which one can use non-Apple software and non-Apple OSes on. Real, actual, genuine alternatives to Apple mobile devices exist in literally every sense of the word "alternative". In that context, that one cannot install an alternative OS on an Apple product is irrelevant and doesn't mean, at all, by any rational measure, that therefore "alternatives don't exist." It's simply facile to suggest otherwise.

What you're failing to understand is that there is more than one market in question. Nobody is saying that Apple has a monopoly on smartphones. The issue is that Apple has a monopoly on iOS app distribution. It's a completely different market, and there is no substitute product in that market. You can't get iPhone apps from Google Play and you can't run Android apps on your iPhone.

No, the market is "consumers of mobile devices, upon which apps can be distributed or installed." What you're identifying as it's own market is actually a brand; a segment of a larger market. A market in which there is plenty of competition, I'd add.

What you're proposing could easily be said about any supply of any good or service owned by anybody or any company. If each company's product distribution constitutes a monopoly of "Product X Market", then "monopoly" has been redefined.

I'm not arguing that what Apple has done in the mobile space is good, or even ethical or appropriate. I'm simply arguing that they do not own a monopoly, in any sense of the word that is reasonable in this context.

> No, the market is "consumers of mobile devices, upon which apps can be distributed or installed."

Let me see if I can explain why that's wrong.

> What you're proposing could easily be said about any supply of any good or service owned by anybody or any company. If each company's product distribution constitutes a monopoly of "Product X Market", then "monopoly" has been redefined.

Technically a trademark is a monopoly, albeit a legally granted one. But that's not what I'm talking about.

For example, Exxon 87 unleaded gasoline is completely fungible with BP 87 unleaded gasoline. They're for all practical purposes the same product, so they're in the same market even though they're different brands. An iPhone is less fungible with, say, a Samsung phone. They're still close enough substitutes to be plausibly considered the same market (although, for example, in the Microsoft case Windows and MacOS were found not to be in the same market). But that's still not the market I'm talking about. I'm talking about distribution of apps for these devices.

Let's start with a preliminary issue. Are iPhone apps in the same market as Android apps? Can they be used as substitutes for one another? The answer is clearly no. You can't run an Android app on an iPhone. This is substantially why Windows and MacOS were found not to be in the same market, but again that's not the market I'm interested in here. The point is that iOS apps and Android apps are not substitutes. And that doesn't even necessarily separate the markets for the devices -- because even though Angry Birds for iOS is a different product sold to different customers than Angry Birds for Android, the fact that the quantity and quality of apps available for each platform is comparable means that the platforms themselves are still reasonable substitutes for one another. But you can imagine how that could change if app developers stopped developing for one platform or the other, which reinforces the point.

So back to the apps. Is there competition for the production of iOS apps? Of course there is. There are thousands of developers; that's not at issue. But distribution is different than production. General Electric is not Walmart. Is there competition for distribution? No. No one is allowed to distribute iOS apps but Apple. There are no substitutes, Apple has a distribution monopoly in that market.

That is not how most "brands" work. You don't have to buy cars through Exxon. You don't have to buy gasoline through Ford. You don't even have to buy Android apps through Google Play. Apple is doing something unusual which results in the monopoly.