The Prisoner's Dilemma
The prisoner's dilemma was originally formulated by mathematician John Nash and has since become the classic example of a "non-zero sum" game in economics, political science, evolutionary biology, and of course game theory.
A "zero sum" game is simply a win-lose game such as tic-tac-toe. For every winner, there's a loser. If I win, you lose. Non-zero sum games allow for cooperation. There are moves that benefit both players, and this is what makes these games interesting.
In the prisoner's dilemma, you and Albert are picked up by the police and interrogated in separate cells without a chance to communicate with each other. For the purpose of this game, it makes no difference whether or not you or Albert actually committed the crime. You are both told the same thing:
At first glance the correct strategy appears obvious. No matter what Albert does, you'll be better off "defecting" (confessing). Maddeningly, Albert realizes this as well, so you both end up getting four years. Ironically, if you had both "cooperated" (refused to confess), you would both be much better off.
And so the game becomes much more complicated than it first appeared. If you play repeatedly, the goal is to figure out Albert's strategy and use it to minimize your total jail time. Albert will be doing the same. Remember, the object of the game is not to screw Albert over. The object is to minimize your jail time. If this means ruthlessly exploiting Albert's generosity, then do so. If this means helping Albert out by cooperating, then do so.
To make this game more fun, I've given Albert several different strategies that were inspired by a chapter in Carl Sagan's book, Billions And Billions: