In the high-stakes game of brinkmanship, pharmaceutical giant Novartis (NYSE:NVS) has dared the target of its takeover bid Chiron (NASDAQ:CHIR) to blink.

Earlier this month the pharma made a $40-a-share offer for the flu vaccine maker in which it already owns 42% of the shares. Chiron had approached Novartis to see if it might be interested in acquiring the remainder of its stock, which has had trouble gaining traction in the wake of Chiron's vaccine contamination problems.

Being able to produce at most only half as much vaccine as it had been prepared to deliver last year, Chiron was now facing new entrants in the market. Though vaccines are a sizable component of its revenues (some 24%), its blood-testing and biopharmaceutical segments remain larger in comparison, coming in at 31% and 36%, respectively. Chiron remains a valuable business.

Novartis apparently thought so, too. It has long held a stake in Chiron. At one time it approached 50% ownership, but that has been scaled back slightly in recent years. Yet with competitor GlaxoSmithKline (NYSE:GSK) moving to acquire rival flu-vaccine maker ID Biomedical (NASDAQ:IDBE) and entering the vaccine market in a big way on its own, the chance to bolster its position undoubtedly moved Novartis to make the bid.

When Chiron's independent board of directors rejected the $4.5 billion offer as "inadequate," analysts were not surprised and expected Novartis to up the ante.

The pharma did just that. Novartis CEO Dan Vasella let it be known that he was quite willing to walk away from the offer. "If I'm known for anything," he said, "it's that I am not afraid of walking away from a deal."

That was in evidence last year when Novartis walked away from a "white knight" bid to counter French pharmaceutical Sanofi's (NYSE:SNY) hostile bid for Aventis. Although the two companies had been in talks on a possible purchase price above the lowball $56 billion Sanofi bid, Novartis walked away from even naming a purchase price when it was clear the French government was adamantly opposed to a Swiss takeover. Sanofi eventually upped its offer to a more palatable $65 billion at the urging of the government, and an arm-twisted Aventis accepted.

Now Novartis hasn't said it won't up its bid for Chiron. The company merely commented that it has a "walk-away price," an offer it's willing to go up to, but no more. But, as if to underscore to Chiron's board that it should not get greedy, Novartis has pushed the envelope -- saying that should the deal fail, it might even consider selling its 42% stake.

The ball is back in Chiron's court. The $40-per-share bid, while not a kingly price, is also not an attempt to buy the company on the cheap, either. The question is, does Chiron dare not blink and possibly lose its largest investor, or will it accept an offer that it closer to the original bid? Though I originally felt a new offer by Novartis might be in the range of $44 to $46 a share, my thinking is that a final agreement might now be accepted at the lower end of that range.

While they both need each other, and the partnership has been good (other than the vaccine debacle), Novartis can look to other acquisition candidates in the market. Does Chiron have the wherewithal to go it alone?

Fool contributor Rich Duprey does not own any of the stocks mentioned in this article. The Motley Fool has a disclosure policy.