If you give a discount, how much?
As a independent contractor this is completely in your control! Some sitter's do others do not!
I do not provide discounts ever. That's my personal choice, of course. I do this for a living so I really depend on what I earn. I try to keep my rates at an even amount that I think is fair. It's what I'd be willing to pay someone to watch my dog. Part of being a responsible pet owner is making sure you have the resources to make arrangements for your pet(s) when you go on vacation.
I do but I make it a package they purchase up front. That way I have payment FIRST and they get their discount as they continue to book. People will drop out but at least you got paid for the work you did. I give 10% on a 30-visit package.