Their usual strategy is to enter a new market, and pay drivers a higher rate and charge customers a lower rate (or provide discounts and coupons) to encourage growth. Once they're established, adjust those rates until they balance supply/demand.
Uber gave a month of free rides (~$25 limit I believe) when they came in my market a few years ago. Lyft had gotten their the month before and only offered like 3 free rides. They were crushed.