In this increasingly competitive segment of the transportation industry, both startups and stalwarts are launching marketing blitzes leading up to a holiday when demand for rides can exceed the supply of drivers. Cab companies, which have seen customers and drivers flee to the app-based ride companies, are girding for battle on New Year’s Eve with special promotions to underscore that their prices never rise. [...] they cannot because they are regulated. “There’s a massive PR war going on right now, and New Year’s Eve is a really important time,” said Jan Dawson, chief analyst of consulting firm Jackdaw Research. Flywheel, which provides an app for users to summon taxicabs with their smartphones, will offer a flat $10 rate for all Flywheel-summoned cab rides within San Francisco from 8 p.m. Wednesday to 3 a.m. Thursday. While Flywheel doesn’t have the massive war chest of Uber, which has raised about $3 billion, it has a respectable $30 million in venture backing, including a recent $12 million round. “I’m happy (to spend) a lot of money because it will get a lot of people using taxis and Flywheel,” Mathur said, likening the struggling cabbies to “Return of the Jedi” underdogs. “Transparent, predictable pricing is one of the things that distinguishes us from the new ride services, who charge pretty much whatever they want,” said Charles Rathbone, Luxor assistant manager. Uber held a press briefing on Monday to explain its position that its surge pricing — which it calls dynamic pricing — isn’t a form of gouging. In keeping with its warm-and-friendly image, Lyft’s promotion centers on the fact that co-founder and President John Zimmer will take to the wheel as a Lyft driver on New Year’s Eve, with his mother as co-pilot.