DALLAS » While corporate travelers have been grounded by the slow economy, a lot of vacationers have still been renting cars. That says a lot about why Hertz and Avis are fighting over Dollar Thrifty, a chain known for lower rates that appeal to leisure travelers.

Dollar Thrifty Automotive Group Inc. has accepted Hertz’s latest bid of about $1.56 billion for the chain. That would top Avis’ latest offer of more than $1.3 billion.

Whoever wins the fight for Dollar Thrifty, renting a car or SUV on vacation might cost a bit more.

Fred Lowrance, an analyst with Avondale Partners, said the number of cars offered by a combined Hertz and Dollar Thrifty would be smaller than the two companies’ current fleets. That could lead to higher prices for renters.

"You’ll have some fleet coming out of the system, kind of like what we see with the airlines, and as travel demand comes back, you’ll probably see some increases," Lowrance said.

Jonathan Weinberg of AutoSlash.com, which tracks the rental business, says car renters have been suffering sticker shock because the recession forced the companies to cut back on fleet upgrades and keep cars longer.

"So you end up paying more and you get a car that’s older," he said.

The rental business peaked in 2007 at $30 billion in revenue. It struggled after air travel — a primary source of rental-car customers — slowed significantly the following year. Revenue should reach roughly $25 billion this year, according to research firm IBISWorld.

Enterprise controls about 37 percent of the U.S. market, followed by Hertz at 20 percent, Avis Budget at 17 percent, and Dollar Thrifty at less than 7 percent, says IBISWorld.

The industry has been consolidating for several years. Avis and Budget were spun off by their former owner as Avis Budget Group Inc. in 2006, and Enterprise bought National and Alamo in 2007. Now Hertz wants to add the Dollar and Thrifty brands to its business.

"The Dollar Thrifty value segment perfectly complements Hertz’s business, which is premium business and leisure," said Neil Abrams, a former Hertz executive and now a rental car consultant in Purchase, N.Y.

For Avis, the strategy is simple, Abrams said: "They don’t want Hertz to get Dollar Thrifty," which competes against Avis’ Budget Rent A Car brand.

Hertz argues that if Avis were to buy Dollar Thrifty, it would control more than half the value market, which could cause antitrust regulators to question such a deal. To avoid any regulatory hurdles for its own deal, Hertz is conducting a sale of its Advantage value brand. Advantage is far smaller than Budget, Dollar and Thrifty.

Dollar Thrifty said late Sunday that its board accepted Hertz Global Holdings Inc.’s new offer of $50 per share, up from the $41 per share it offered in April. Including restricted stock and stock options, the offer is worth $1.56 billion, according to a Hertz spokesman. The new offer includes $43.60 in cash plus 0.6366 of a share of Hertz common stock and $6.87 per share to be paid by Dollar Thrifty as a special cash dividend before the deal closes.

Dollar Thrifty would get a $44.6 million reverse breakup fee if Hertz backs out. Avis’ last offer for Dollar Thrifty was $1.3 billion in cash and stock, or more than $47 per share. Some Dollar Thrifty shareholders protested the board’s rejection of the Avis offer, but the board discounted the Avis offer for lack of a breakup fee and said it didn’t adequately address antitrust concerns.

Dollar Thrifty, headquartered in Tulsa, Okla., delayed a special shareholders meeting to vote on the Hertz offer from Thursday until Sept. 30.

Credit rating agency Moody’s Investors Service, meanwhile, said it is reviewing all its ratings on Hertz for possible downgrade, affecting about $1.8 billion in debt. Moody’s said it expects the Dollar Thrifty acquisition to bring significant long-term benefits to Hertz but said it is concerned that the funding for the deal could put a strain on Hertz’s ability to maintain its current credit profile.

Dollar Thrifty shares rose $2.67, or 5.4 percent, to $50.58. Avis shares climbed 73 cents, or 7.1 percent, to $10.95, while Hertz shares gained 79 cents, or 7.9 percent, to $10.84.