Blackstone Group LP's preliminary bid to take over Dell Inc. is setting the stage for a rare event: a bidding war between private-equity firms.

Blackstone, the world's biggest buyout firm, and activist investor Carl Icahn made separate offers last week that rival a $24.4 billion bid for the computer maker by Dell founder Michael Dell and Silver Lake Management LLC, according to a statement today from Dell. The shares rose 3.2 percent to $14.59 at 9:31 a.m. in New York, 6.9 percent above the Silver Lake offer.

While competition for buyout targets is often vigorous in the early stages of auctions, private-equity firms, which buy companies in expectation they can sell them later at a profit, are usually reluctant to make competing bids once a deal has been agreed. Go-shop periods, during which the buyout target can solicit competing offers after the initial agreement, too often are cosmetic affairs that give bidders little time to mount a challenge, said Erik Gordon, a business and law professor at the Stephen M. Ross School of Business at the University of Michigan in Ann Arbor.