A person should make it very clear in his or her invitation whether the suggested dinner or drink is a “treat” or whether the bill will be split among the members of the group. You can do the former by saying, “I’d like to invite you to dinner (drinks) on Tuesday.” From this, it is clear that the dinner or drinks will be paid for by the one who suggested it. You can do the latter by suggesting, “Shall we get together for dinner on Tuesday, Dutch treat?”
Unfortunately, life is not always so clear cut. Invitations such as “How about a drink after work?” or “Would you be interested in going to lunch on Saturday?” leave open the possibility that the person suggesting the event is only planning on paying part of the bill.
When you are leaving the restaurant, it is improper to argue over who will pay the bill. If another person picks up the check, let him and be grateful for the treat. Close friends may offer to leave the tip, but this requires knowing what the total bill is, so doing this is problematic. Rather than an unsightly grabbing for the bill or insistence on paying the tip, it is better to allow the inviter to pay, then thank him or her outside. There will always be opportunites for reciprocating.