Nintendo literally had the opportunity to own the entire console gaming industry, but passed it up...
Prior to the original Playstation, Sony was actually working for Nintendo developing a prototype that could bring CD media to the SNES. Long story short they had a disagreement, Nintendo basically said forget it, so Sony just went off and revised their creation to be what became the original Playstation, see this link.
So if Nintendo would have been a little more lax, and gave Sony the deal they wanted, they would have actually been partners.
Then Microsoft actually approached Nintendo about partnering up(just before they made Xbox) and Nintendo said no, so as a result Microsoft made the original Xbox on thier own. See this link.
Had Nintendo appreciated Sony more, and was willing to work with Microsoft, there would be no Playstation or Xbox, but instead they would have both Sony and Microsoft working under their umbrella of what would be industry dominance. But instead they are competing with both brands which have proved to be quite the powerful foes in this sometimes harsh industry.
+ Microsoft = What could have, but will never be...
I have contemplated this for a long time now. A big factor that many overlook when analyzing what went 'wrong' with Nintendo can definitely be held to the Japanese culture and decisions made by previous Presidents.
The 3rd President of Nintendo, Hiroshi Yamauchi, was in charge at the time of the disputes between Sony and Nintendo. He is accredited to taking Nintendo from small card-making company to the multi-billion dollar company that we see today. Without his guidance, who know's where Nintendo would be today. To return to my point of Japanese culture, typically (although constantly changing from generation to generation) the Japanese people can be classified into the same category; a low-context culture, with a very traditional, humble and proud society that strongly take prides in their work. The decision of Yamauchi to reject could be argued to save pride of the work that he built up himself since 1952. Whilst you argue that the decision ultimately hurt the company, we could not anticipate what would happen between the two companies in the two decades since the release of the PlayStation had Nintendo agreed to work with Sony. If said scenario had panned out, we don't know where licensing and copyright issues would fall between the two giant companies when it came to Nintendo's notorious ownership of the Pokemon, Super Mario, Smash Brothers, Zelda and more.
After the 3rd President resigned, he passed on the reigns to Saturo Iwata which began the time of the Nintendo DS and Wii product lines. Since then, we've seen the decline of the company as it continuously loses its gaming market shares to Microsoft and Sony everyday, unable to keep up with the console races. However, when President Iwata passed away and the new President, Tatsumi Kimishima (former President of Nintendo of America), took office, Nintendo wanted to switch directions and go where they should have been all-along.
As many have heard by now, Nintendo is working on producing their own console, the Nintendo NX, that is being designed to completely out-do the PlayStation 4 and Xbox One in as many aspects as possible. While news of the impending console is far out, its hopeful as to what Nintendo can produce, if they can tap into the customer base of Microsoft or Sony, and if the console will do wonders for the value of the company. My only regret after all is done, is that I have yet to invest in Nintendo and I'm strongly considering it in light of their new console.
My biggest problem with Saturo Iwata's reign was sacrificing shares in RARE simply for extra money to put towards Research and Development, that eventually led to the Wii. How could I have a problem with that being that the Wii was Nintendo's most successful console? With the Wii U they decided to essentially ditch all that R & D value, and throw motion gaming as an often optional, secondary function no different than what any platform currently offers. Wii opened up to a new audience. Naturally that same audience has upgraded their TV's from SD to HD over time. The Wii was not about physical power at any point, and I know they wouldn't have sold as much of a Wii HD (hyptohetical, powered up but otherwise identical console to the Wii) as they sold the original Wii, but a lot of those same people would have upgraded, rather then family's of new gamers giving up on it when they saw they had to learn the Wii U's touch pad. They lost a lot of customers. The new customers acquired by the Wii all just stick with the original, to the point Wii. The hard core gamers flocked to Sony and Microsoft for third party support, shear power, and better more developed online environments in general. If they were going to leave motion gaming as a secondary function rather then continue to embrace it, they should have gone all out accommodating the core gaming audience.
So how does this relate to Rare. I understand R & D is important, necessary, and helps big companies make informed decisions, but for a company that big to need to sell assets in order to fund the current R & D project, is just more then necessary. Most significant changes occur after the R & D period anyway. Look how Xbox One changed from an online only, no disc sharing, non backward compatible, mandatory Kinect, etc. Into the Microsoft version of what resembles what PS4 has been all along + Micorsoft's own features and games of course. All those changes were due to public feedback/seeing what worked sooo well for Sony compared to what they were doing, not R & D. Nintendo would have wound up with more or less the same Wii without spending sooo much on R & D, and they would still have RARE. RARE is just the kick(well one of the kicks anyway) that Nintendo needs right now. Perfect Dark games, Better 3D adventure Donkey Kong Games, The Banjo Kazooie series where the fan base is and what ever else RARE would have come up with to aid Nintendo, had they not been owned by Microsoft since Nintendo gave up their shares.
NX was a great idea, but unfortunately by making it's existence public information way ahead of time to keep investors interested in the company, I suspect one thing led to another and it eventually, indirectly led to Sony and Microsoft making thier own powered up consoles that will be released during the same time period, and by the sounds of it, Microsoft's will be more powerful then the NX. NX will regain 3rd party support, introduce "a new way to play", and hopefully prove Nintendo learned from Wii U's short falls.