Does it really matter? Do they need a browser at all? Browsers are all pretty much interoperable now. What strategic advantage is there in developing and maintaining their own browser? Nobody pays for browsers. They might pay for content or apps delivered in the browsers. That's what Microsoft should worry about. They've lost their browser monopoly, move on.
You maintain your own browser so that you can influence the development of the web. For example, Apple used Safari's influence to push touch events, Microsoft tried to use its influence to standardise pointer events, Google's been pushing NaCL, Dart etc.
In order to consistently have weight with changing CSS, HTML rendering etc you basically need your own browser - and most of the changes we've seen in the last few years have come out of Google, Mozilla, Microsoft, Apple.
There is also the issue of your army of tech staff doing demos and presentations using your competitors tools, or shipping your operating system with somebody elses browser installed.
With the browser so ubiquitous, it has become a huge part of your platform experience. Consider IE's big power consumption advantage. If people spend all their time in the browser, offering a browser that makes Windows work as well as possible, is good for Windows.
> What strategic advantage is there in developing and maintaining their own browser?
You hold the keys to the default search engine for that particular browser, to name an example. Even with the Mozilla-Yahoo deal it's still in MS interest to own a browser so they can push Bing and their other cloud services there.
the answer from "silverstorm" is correct. To elaborate a bit, if you add a feature or API to the underlying OS, but there's no corresponding browser feature that makes use of it, to someone who spends most of their time in a browser the OS feature may as well not exist. Microsoft's main reason for investing in IE has generally been to try to add to the perceived value of Windows by making new Windows features accessible through the browser and thereby more relevant to web-centric PC usage. Examples are taskbar integration in Win7, live tile support in Win8, the emphasis on hardware acceleration in IE9+ (which was designed to try to make the underlying Windows graphics system more relevant to web browsing), smooth touch panning/zooming in IE10+ (by being early adopters of the Windows DComp/DManip APIs), better font rendering on high-DPI displays via DWrite etc.
Note that if other browsers themselves adopt new Windows APIs in competitive response, that actually still benefits Microsoft because ultimately they don't care about the browser for its own sake, they care about increasing Windows API and feature usage across all browsers. But in practice competing browsers tend to be late adopters of new Windows stuff (e.g., even now nothing but IE supports DComp/DManip and Chrome is just very recently getting around to improving its Windows high-DPI and text rendering support), hence Microsoft funds IE.
