The blame game is the tradional game played by most of the world most of the time.
If you have an unfulfilled need you expressed by making someone else (or yourself) wrong.
[It also works when you attribute your fulfilled need by making someone (or yourself) right.]
Do an exercise. Read a newspaper and notice every sentence or expression, in which you can sense the writer expresses a blame about something or someone. Stop and simplify the blame, so it becomes as clear and concise as possible.
Put yourself in the shoes of the person that is addresses by the blame and image how you would react to this communication. Highly likely you will respond with blaming the other person back.
Talk-shows give excellent examples of the blame game.