The "blame game" is a form of narcissism.
Learn a bit about this condition before you implement any plan of action as this may influence how you decide to handle this situation -
A few points to consider.-
1) "blamers" often do this as a defensive mechanism because of their own insecurities.
2) Blaming can be a form of control. For people who blame, it’s a way of avoiding external repercussions and blamers seek something from their victims, whether it is emotional, monetary, fun, reassurance or psychological stability.
3) the act of blaming can be a difficult behavior to change because it can become very self perpetuating when it is reinforcing itself in the blamers mind each time the tactic is used.
4) often, when thing really bother us about others, it is because it reminds us of a personal flaw so make sure you are not acting on your own insecurities. (great rule of thumb, first seek to fix yourself.)