Good introduction, nothing new (but the "line-item veto" example is a nice one), but still good to have around.

One thing that made me "wail and gnash" a little :

that everyone is purely self-interested

That's not really the case. Game theory usually consider that everyone is an utility maximizer, but nothing says that the utility function has to be selfish. Utility function can factor well-being and happiness of others in it.

You can apply game theory in cases like a parent-child relation, in which the parent and the child disagree, but the parent still is motivated with the interest of the child. Even in more classical cases, nothing forces the utility function to be selfish and not value the other well-being. Game theory only apply when the agents have different goals, but it can just be "I value my own well-being twice as much as the well-being of the other", which is not "purely self-interested".

It makes me "wail and gnash" because it's a very frequent cliché that rationalists and utility maximizer are necessarily selfish and don't care about others, and it's a cliché we should fight. That say, I understand the a whole part of game theory is about showing how even pure selfishness can, in some cases, lead to cooperation being the best solution. Your "line-item veto" is a good example of it, Clinton and Congress can still cooperate to get the previous 5-5 equilibrium, if they trust each others, and this is an IPD at the end.