The Traveller's Dilemma. It's a variation on the Prisoner's Dilemma, but what is interesting about these games is to play them yourself multiple times, and see what happens. We like Game Theory, but the math eludes us as this point.
But it's not just about math - it's about how illogicality can often be logical. Here's the premise:
Lucy and Pete, returning from a remote Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.
Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.
What numbers will Lucy and Pete write? What number would you write?
To keep it simple, play with three people - same as The Prisoner's Dilemma. You play it over and over. Of course, they cannot discuss the strategy together.
