Once again we return to the subject of Sony's finances. Sony's current market cap is about eleven billion dollars, and you can argue that the company is worth more then that or less then that. Sony can value its assets as it sees fit, but the market doesn't have to see it that way. The market decides what the true value of those assets are. Microsoft could make a offer of fifteen billion dollars for the company, and then the investors could decide to accept what is being offered, or they could decline.
Given how willing Microsoft was to walk away from Yahoo. Investors would probably pounce on such a offer as it would mean that the value of their stock would increase by over thirty percent. While declining could actually cause the stock to lose even more value. Even hard bargaining could drive away the prospective buyer. Sony isn't in a good bargaining position. Anything reasonably higher then the current market cap would be pretty hard to walk away from. Especially since the future of the company is fairly uncertain.
That said such a move would be foolish on the part of Microsoft. The reality is that Sony is losing money, because it is a bad product. It makes sense to buy good companies, or companies that stand to have good future growth prospects. What doesn't make sense is to buy a company that is losing money, and is buried up to its eyeballs in debt that the buyer would have to pay back.
That leads us to the most likely scenario for Microsoft beating Sony in Japan. Sony could end up conceding their home market, because they have to focus their comparatively meager resources on markets that offer greater profit potentials. Japan accounts for less then fifteen percent of the global console market, and North America alone is three times larger as far as hardware is concerned then Japan.
That is less of a problem for Microsoft. They can adequately play the entire field. Unchecked Sony's momentum might allow them to slide in Japan without actually aggressively courting that audience, but Nintendo is a home town team, and Microsoft would definitely use such a apathy to their advantage. I mean if Sony isn't aggressively courting domestic developers. You can bet Microsoft would be more then happy to take up all of that slack.
That brings up a good question. How much effort does Sony need to expend to keep their position in this market, and don't tell me no effort at all. Outright neglect would have a truly disastrous impact on the public perception. It is kind of the reverse of the main question, but it does matter for this discussion.