This is a famous problem and scientists have spent years studying this problem and its implications. It was originally proposed by Robert Axelrod (Axelrod and Hamilton, 1981.The Evolution of Cooperation. Science 211: 1390-1396.), a political scientist. Axelrod proposed a tournament in which people could submit different strategies would compete to see which ones fared the best against the others. Although no one strategy is the best in all cases, some fare better than others. Some of the key players (not necessarily the best) to emerge from this, and subsequent contests are:
Try pitting some of these strategies against each other. Start with a single interaction, and try increasing this value through about five interactions. There may not be one best strategy. Some may do better against one strategy, but worse against another. How might this affect evolution? Can you come up with a behavioral interpretation of any of these strategies?