How to handle siblings of guests at child's party?

I am having my daughter’s birthday party at the bowling alley (yeah, yeah… it’s what she wants) and will be inviting her friends. The issue I am having is how to handle the siblings of her friends when they inevitably show up.

She will be 4 and most of her friends have brothers or sisters. Older siblings will be in school, but younger siblings certainly will be there with the parents. Some will be too young to participate, others are questionable. A 2½ year old can “bowl” with the bumpers and the ramp/stand.

I don’t mind making sure there is enough pizza & cake for them, but each bowler is $7.25. If all of the siblings show up and play then the cost of the party goes up quite a bit.

Should I bite the bullet and pay for them or is there a tactful way to let parents know that only the child specifically invited is paid for and they need to pay for any additional children they bring along?