How we don’t always act rationally.  Prisoners dilemma: if both confess, both go to jail.  If one confesses then he goes free and the other goes to jail.  But if neither confesses then both go free. The paradox is that self interest will drive both to confess, even though the best outcome would be achieved by neither confessing.
Hawk and Dove game (Maynard Smith and Price)  – 2 players competing for a resource, can choose to be hawk or dove.  If both hawks then violent confrontation with poor outcome for one.  If both doves then shared.  But if one hawk and the other dove, then best outcome for the hawk.  Variation of Chicken! (2 cars driving towards each other, with poor outcome the label of Chicken!.  Shows how mixed strategy of cooperation with intermittent selfishness (aggression) is best.
Ultimatum game – if 2 find money on the street, and 1 has to offer a share to the other which if rejected means neither gets. self interest would suggest that even a trivial share should be accepted yet sense of justice means at least 25% should be offered, and actually rises as game repeated!
Lots of this work done by John Forbes Nash (A Beautiful Mind) eg Nash equilibrium.
From In our time (BBC Radio 4)