Within the past three weeks the chief executives of Microsoft and Yahoo! have said that the best thing for both companies is for them to do the much-discussed takeover deal.

So the question today for Steve Ballmer and Jerry Yang, after Google pulled out of its online advertising partnership with Yahoo!, is: “Why don't you just get on with it?”

Both companies insist that there are no talks under way but, certainly from Mr Yang's point of view, there is no downside to opening discussions again. Perhaps that was his intention when he issued what amounted to a plea to Mr Ballmer at the Web 2.0 Summit in San Francisco.

Mr Yang said: “To this day, I would say that the best thing for Microsoft to do would be to buy Yahoo!. Did we want to do the deal? Yes. People who know me know I don't have an ego about remaining independent. We remain open to everything but it has to make sense.”

Clearly, Mr Yang has to do something. He lost the confidence of the tech community some time ago and support among investors is ebbing fast. It should be remembered that consumers still love Yahoo! It is a huge brand and second only in search to Google, but that is no longer enough.

In particular, Mr Yang has failed, as he did again at Web 2.0, to convey a compelling vision for where he wants to take the company.

Yahoo! is back where it was at the start of the year, except now the outlook is decidedly worse. The crumbling economy is discouraging advertisers from spending online, particularly on the billboard-style display ads that are Yahoo!'s bread and butter.

Yahoo! said that it would lay off 10 per cent of its workforce after profits plunged 64 per cent in the most recent quarter and, perhaps even more worrying for investors, it is also leaking senior staff.

Most agree that a full takeover by Microsoft is probably not the best option. It is difficult to imagine an easy or painless integration into the corporate culture of Redmond by the purple Yahoos of Sunnyvale.

Microsoft proposed in the spring that it should buy Yahoo!'s search operations and it is more likely to want to return to that.

The result would be cost savings for Yahoo! and more energy to focus on the display ad business. Analysts estimate that Yahoo! would make a net gain of $725 million (£460 million).

Perhaps Yahoo! could go shopping for smart acquisitions itself among struggling, and cheap, start-ups to revitalise its businesses — an idea Yang discussed on stage.

The problem is that Microsoft has nothing to lose from waiting while Yahoo!'s problems continue and its share price dives farther.

The software maker has little incentive to raise its bid of $1 billion that it offered in the spring.

An alternate possibility for Yahoo! is to acquire at least a slice of Time Warner's AOL. Melding two companies seen as dot-com has-beens is unlikely to yield a new powerhouse, but such a deal could augment Yahoo!'s display advertising business.

AOL operates Platform-A, the largest ad network in the US, which lets advertisers buy display ads across AOL's own sites.

However, AOL's online advertising business is not as lucrative as Google's or Yahoo!'s despite its wider reach, and its ad revenue fell by 6 per cent in the third quarter. Talks about a tie-up have been going on for months and Mr Yang declined to discuss them at the Web 2.0 Summit. “I could tell you, but I'd have to kill you,” he said.

On the search-advertising side, Yahoo's potential gains from an AOL acquisition are also unclear. For one thing, Google, which owns a 5 per cent stake in AOL, operates AOL's search — presumably raking in more money than Yahoo! could get if it took over.

Buying AOL could, ironically, make Yahoo! a more appealing target for Microsoft, especially if the buyout went badly. Microsoft could wait a few months, then vacuum up two competitors, which still attract large online audiences, at a bargain rate.

Microsoft, in other words, holds all the aces.

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