But in 1999, it was bought by Bernard Arnault, head of LVMH, for $113 million, with the goal of making it a high-end alternative to Sotheby's Holdings Inc. and Christie's International Plc. To do that, Mr. Arnault has been funneling millions of dollars into the business, some of which is basically being used to buy the art it auctions. "They are like a young dot-com trying to buy market share," says Frederic Cooper, assistant general counsel at KPMG and a Manhattan-based collector. Phillips has the luxury of behaving like a start-up, but with the full and generous backing of LVMH. "Right now, if a specialist comes to me with a deal, we go out of our way to back him up financially," says John Block, named in January as Phillips' new chief executive of North and South America. Though its strategy may be risky, Phillips' attempt to grab market share could not come at a better time. Sotheby's and Christie's have never been more vulnerable.