Umm, I have never had to do that before. But it depends on the situation. If I am the host and I have less resources, I would rather not have a birthday party in a restaurant where my guests have to pay for their food. I would rather have it at home and may be have my family help me to celebrate. It is a different situation when you are having a get together lunch.
Now coming back to would I pay, it depends on how close I am to the host.
Well I think it depends on how the invite is worded - if the birthday person has said "would you like to come out for a meal, I'm celebrating my birthday" then I would expect to pay and be quite happy to do so. If the invite was more along the lines of "I'm having a party at this restaurant" then I wouldn't expect to pay.
I have actually heard of this and have actually done it myself.
Most years I go to an expensive buffet for my birthday and a handful of friends come along and we all pay for our own meals. Otherwise we would not do it as it would just be too expensive for me to pay for it on my own.
So I have heard of it and have done it,though we do it with females in the day and I would not do it with mixed sexes at night -no idea why this is not OK and the first one is!
I was invited to one of these birthday parties and did not know until a few days before that I had to pay for my meal I had been commenting to my family that it was going to cost the daughter of the birthday girl a very large amount of money, just as well I was told a few days before by someone else attending we all had to pay , as I would not have had the money with me.
if a girls lunch or dinner out for a birthday etc
we always pay for the guest person.