AT&T; Offers $100 Enticements : Telecommunications: It’s the latest gambit in an effort to lure customers away from rivals MCI and Sprint.

What would it take to get you to switch your long-distance telephone company? A 20% discount on calls to your 12 closest friends? A month or two of free calling? How about cash?

How about $100?

AT&T;, the nation’s largest long-distance carrier, has recently begun sending $100 checks to a small number of customers of rivals MCI and Sprint in a bold effort to persuade them to switch to AT&T.; If customers cash the checks, AT&T; is automatically authorized to switch their service from MCI, Sprint or other long-distance companies.

AT&T; notes that the $100 checks have recently been mailed to “a very limited” number of residential customers in unidentified test markets in an experiment designed to determine the level at which “persuasion is the most effective.” For the last eight months, AT&T; has routinely mailed checks of $10 to $50 to competitors’ customers to get them to switch companies.

“The real question is, ‘What’s your price?’ ” an AT&T; spokesman said. “Everyone has one.”

AT&T;’s latest gambit represents a significant upping of the ante in the ongoing marketing wars among the nation’s top three long-distance carriers. Sprint and MCI wasted little time criticizing their rival.

“It’s a desperate move to buy customers,” said a Sprint Corp. spokesman.

“They have lost market share,” said a spokesman for MCI Communications Corp. “They can afford to try to buy it back in a very high-cost way.”

According to telecommunications market analysts, in the last three years AT&T; has begun to slow its loss of market share to MCI and Sprint, which compete for the nation’s nearly $60-billion long-distance market.

AT&T;, which held 90% of the U.S. long-distance business in 1984, saw its market share shrink to 69% in 1989 and 67% in 1991, according to the Yankee Group, a market research firm in Boston. MCI, the nation’s No. 2 long-distance carrier, controlled about 16% of the market at the end of 1991 and Sprint had 9%.

Still, MCI and Sprint have recently made inroads into the residential market with discount plans for frequent callers, a development that analysts say AT&T; is trying to offset with the rebate checks.

However, according to Sprint, which has tried and dropped a rebate check plan, a one-time offer holds little advantage for consumers--or phone companies.

Once the rebate check is cashed, there is no minimum time a customer must stay with the new carrier, allowing subscribers to switch carriers as often as they want to take advantage of the latest offer.

And with the average residential long-distance bill running about $17 per month, carriers would have to retain customers for a long time to recoup a rebate of $50 to $100.