Southwest Airlines proposed a $100 million deal for some of the assets of the bankrupt ATA Airlines yesterday, raising the stakes in the opening battle for the future of the industry's low-fare market. The offer was $10 million more than a bid by AirTran Airways. AirTran had a tentative deal with ATA when the airline, which is based in Indianapolis, filed for bankruptcy protection on Oct. 26. The move by Southwest was a sign of the competition that is emerging in the low-fare segment of the industry. Low-fare companies are expected to carry about 25 percent of the nation's air travelers this year, up from just 6 percent in 1990. The battle for the assets of ATA pits some of the best-known executives in the industry against each other, namely Herbert D. Kelleher and Gary C. Kelly, the chairman and chief executive at Southwest, and Joseph B. Leonard, the chief executive at AirTran.