To accept such an invitation I would make sure that I was OK with either scenario. There are also cultural differences that would determine the likelihood of paying. I would feel that such an invitation would usually be paid for especially considering the age of the person. Young people and older people I would think an invitation would mean they re inviting you to the dinner. However, for the 18-40 age bracket I would expect to pay for myself.

Having said that I would only accept invitations if I were happy and prepared to pay for myself. Anything else is a bonus.