Yesterday’s volleys between Microsoft and Yahoo (NSDQ: YHOO), though dramatic, pretty much played out as expected. Yahoo scoffed at Microsoft for lowballing its offer and Microsoft professed to be dismayed at Yahoo’s response. Now that the perfunctory opening statements have been read, the two sides can get to the hard part. We already discussed some of the options Microsoft has at its disposal, including raising the bid, going hostile and taking the case to big Yahoo shareholders. All of this is still on the table. The New York Post is reporting that Microsoft has hired a proxy solicitation firm to prepare for a more hostile effort, although even if Microsoft intends to sit down and discuss things with Yahoo, it makes sense for them to keep applying this pressure. Meanwhile, notes MarketWatch, Yahoo’s un-staggered board election, makes the company more vulnerable to pressure. As for what happens next, Wall St. analysts have been updating their predictions:

-- Mark Mahaney, Citigroup: Most likely scenario: Microsoft and Yahoo sit down and hammer out a deal at a new price. The fact that no other bidders have emerged and Yahoo’s board has come up with few other credible alternatives doesn’t give it much fight for other than a higher bid from Microsoft (NSDQ: MSFT). Much less likely scenarios: a white knight emerges (unlikely, because none have), Yahoo unveils a new strategic initiatives, such as a deal with Google (NSDQ: GOOG) (unlikely to satisfy shareholders), and regulators block the deal (which could happen along with the first possibility).

-- Marianne Wolk, Susquehanna: Wolk’s thinking is pretty similar to Mahaney’s, as she assigns a 75 percent probability to a deal happening, and a low likelihood of any meaningful alternative: “At $44.6 bln, Microsoft’s proposed acquisition of Yahoo! is significant. We find very few companies positioned to bid against Microsoft for a deal of this size – in terms of financial resources or strategic need.” Wolk also explains that Yahoo does have a poison pill at its disposal, which it adopted in 2001, but it sounds rather weak in this particular situation. If an acquirer picks up 15 percent of the company, then existing shareholders will be given the right to buy more shares, creating dilution. But considering the premium Microsoft is offering to Yahoo’s prior market price, it’s hard to imagine shareholders rushing out to buy shares in order to stymie the offer.

-- Jeff Lindsay, Bernstein: Despite the letters both companies put out yesterday, the overall tone suggests a desire to talk, rather than to embrace outright hostility. Thus negotiations are likely to occur, or may already be occurring between the two parties. Likely outcome: an offer somewhere in the mid-$30s. He believes Microsoft purposely left itself some upside wiggle room when putting in its first offer and that at a price of $35 per share, Microsoft can still justify the acquisition financially. At $40, however, Microsoft would have a more challenging case to make that it was still getting a good return.

-- Jordan Rohan, RBC: Again, more expectations of a negotiated deal somewhere in the mid-$30s. Yahoo’s board is doing its job by pushing for more: ”Yahoo’s board has spent the past week trying to cobble together a competing bidder to buy the company. When no “white knight” bidder emerged, the company did the next most logical thing, which is to position itself to pry a higher price from MSFT.”

Bottom line: The general consensus is that the two sides will negotiate a deal that splits the difference between Microsoft’s offer and Yahoo’s desire to get somewhere around $40 per share. If Yahoo were to batten the hatches, Microsoft could go hostile, but seeing as Yahoo has little to gain by eliminating the one serious offer for it, Microsoft probably won’t have to—of course, it will go through the motions, just in case it comes to that. The Deal Professor Steven M. Davidoff spelled it out in a message to Yahoo’s board: there’s only so much that the various investment banks and law firms that Yahoo has hired can really do to help the company: “… your options are limited. Throwing yourself on the mercy of Microsoft not to go hostile appears to be another loser of a strategy. And while you can find some tie-up or other maneuvers to stall Microsoft or make any acquisition more expensive for them, it doesn’t look good.”