But this will get their competitive juices flowing. They will know that they'd better make a decent offer quickly if they hope to get the film. It takes some diplomacy to orchestrate a bidding war and not alienate the losers. You want to firmly push each of the potential buyers to offer the best terms possible while maintaining cordial relations. After all, you may want to do your next project with one of the losers.
Filmmakers know about film, distributors know about distribution.
Don't kid yourself and think you can play in the other guy's arena and win. Retain an entertainment attorney or experienced producer's rep to advise you and negotiate your deal. I have seen filmmakers give their premiere away to minor festivals and thereby disqualify themselves from major ones. You can play in the lesser festivals later. If you get turned down by an important festival, the worst that happens is that your suffer a small delay in your release plans.