Relax guys, you can get along now. Image Source: Flickr user Tsahi Levent-Levi

When it comes to the smartphone industry, we tend to think of competition as a zero-sum game. And in some cases that's apropos -- as far as device sales go, one vendor's market share gain typically comes at the expense of another's, making summations and comparisons easy to discuss among hardware manufacturers. While market share growth doesn't always directly translate to profit growth, it's a positive sign for manufacturers.

When it comes to operating systems, however, direct comparisons are less beneficial. That's because the two largest operating systems, Google's (NASDAQ:GOOG) (NASDAQ:GOOGL) Android and Apple's (NASDAQ:AAPL) iOS, took decidedly different routes for growth. Apple chose the closed ecosystem route, only allowing iOS on the company's own products. Google, on the other hand, made Android an open-source OS available to numerous hardware vendors.

Further complicating matters is the fractured Android market. In the U.S., Google is mostly able to control its Android OS through a system of APIs vendors need for third-party app support. In China, however, Android has been modified -- or "forked" -- giving it decidedly less control of its own ecosystem.

Long story short: An Android user isn't the same for Google as an iOS user is for Apple. But for Google, Apple's growth provides a symbiotic relationship of sorts, and in Asia, Google's in a position of rooting for Apple and its more affluent users rather than the "partners" who use Android to advance their own goals at the expense of Google.

Google's mobile strategy is dependent upon Apple
According to investment bank Goldman Sachs, Apple's iOS appears to be more important to Google's mobile strategy than is Android. Goldman's analysis (courtesy of The New York Times) found Google collected $11.8 billion on mobile search ads in 2014, with 75% (roughly $8.9 billion) of that coming from ads on iPhones and iPads. The Times credited more affluent iOS users who spend more time on their phones. Assuming the rest of the money came from Android devices, which should be accurate considering the mobile OS market is a virtual duopoly, mobile search from Android devices only generated $3 billion (differences due to rounding).

One could argue that's only search, and a true comparison of Apple's importance to Google's mobile strategy should also incorporate Android app sales. The article also found that Google sold about $10 billion in apps in2014, but only kept $3 billion of that on a net-sales basis (for a great primer on net versus gross sales, read this article from colleague Andres Cardenal). Adding this $3 billion to the $3 billion Google earned from mobile search on Android devices shows the company earning $6 billion of mobile revenue from Android and nearly $9 billion from iOS.

In Asia, is the enemy of my enemy my friend?
This makes for a weird dynamic in some Asia-Pacific countries. On one hand, companies such as Xiaomi use a forked version of Android, so you'd assume they would be natural partners for Google. And you'd be wrong: Xiaomi essentially treats the phone as a loss leader of sorts to make money with its apps that compete with Google's apps. The company has also put a dent in the sales of full Android device vendors such as Samsung. On the app download side, Google is only nominally better with Asia's forked Android vendors than it is with Apple sales in which it receives nothing.

Outside of mainland China, which essentially bans Google Search, an intense fight for mobile search revenue and OS dominance persists in the region. While Apple has fewer OS subscribers in total, they are inherently more valuable to Google from a search standpoint. Of course, this is because advertisers understand that iPhone and iPad users on average have higher incomes, but Asian iPhone growth also could imply a "trade up" from low-cost Android units, signifying more disposable income. Not to mention Xiaomi already has a strong relationship with Chinese search engine Baidu, which is looking to expand into more countries.

In the end, the choice for Google in Asia is to root for a competing OS that bolsters your core search business or forked "partners" that want to essentially undermine your OS's business model.