Just as the Sirens of Greek mythology lured sailors to their doom on a rocky coast, China’s fast-growing Web has drawn Western companies to its shores, where they have seen their business hopes dashed in a treacherous market. Until recently, eBay was among the disappointed. Eight years ago, it paid $150 million to buy China’s top e-commerce site, EachNet, then plowed an additional $100 million into its operations. But it was foiled by local rivals who offered similar services for free. In 2006, eBay handed over its operation to a competitor in a joint venture. But eBay, based in San Jose, Calif., reinvented itself in China by turning to a model that is helping it and its online payment business PayPal navigate the new Internet world. A few years ago, the company quietly resurrected its China business by letting exporters of everything from wedding dresses to camera equipment sell directly to eBay’s 97 million overseas users. “We asked ourselves, ‘How can we participate in the Chinese e-commerce market?'” said Jeff Liao, CEO of eBay Greater China. “The answer is so obvious: Play to our strengths, leverage our global franchise.”