If you have access to the Wall Street Journal, there is a very interesting article in today's (27 Oct 05) edition (page A1) about the huge expenses that Bridgestone and Michelin incur on the F1 circuit as well as some history behind both companies.
Here's a paragraph that I found interesting: "In June, for example, blowouts of Michelin tires led seven teams to withdraw from the U.S. Grand Prix, infuriating 120,000 fans and Formula One racing authorities alike and striking a blow to the Michelin brand name. One month later, after a particularly poor showing in a race, the top driver using Bridgestone tires, famed German racer Michael Schumacher, delivered what may be the worst-ever plug for a sponsor: "It's obvious we have to get faster, but our main problem is the lack of grip with the tires. It was like trying to fight with a blunted weapon." To cap it off, racing authorities began openly questioning whether the corporate duel is doing the sport more harm than good."