If I have two objects that have a many-to-many relationship, I would typically model them in my database schema with a many-to-many table to relate the two. But should that many-to-many table (or "join table") have a primary key of its own (integer auto-incremented)?
For example, I might have tables A and B, each with an ID, and a table called A_B that has a foreign key tuple of (A_ID, B_ID). But should A_B have a primary key auto-incremented ID column of its own, or not?
What are the advantages and disadvantages of adding it? I personally like natural keys for many-to-many joins. But what added benefit would a primary key add?